# Keçeci Numbers: Keçeci Sayıları
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---
<p align="left">
<table>
<tr>
<td style="text-align: center;">PyPI</td>
<td style="text-align: center;">
<a href="https://pypi.org/project/kececinumbers/">
<img src="https://badge.fury.io/py/kececinumbers.svg" alt="PyPI version" height="18"/>
</a>
</td>
</tr>
<tr>
<td style="text-align: center;">Conda</td>
<td style="text-align: center;">
<a href="https://anaconda.org/bilgi/kececinumbers">
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</a>
</td>
</tr>
<tr>
<td style="text-align: center;">DOI</td>
<td style="text-align: center;">
<a href="https://doi.org/10.5281/zenodo.15377659">
<img src="https://zenodo.org/badge/DOI/10.5281/zenodo.15377659.svg" alt="DOI" height="18"/>
</a>
</td>
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<tr>
<td style="text-align: center;">License: MIT</td>
<td style="text-align: center;">
<a href="https://opensource.org/licenses/MIT">
<img src="https://img.shields.io/badge/License-MIT-yellow.svg" alt="License" height="18"/>
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</tr>
</table>
</p>
---
## Description / Açıklama
**Keçeci Numbers (Keçeci Sayıları)**: Keçeci Numbers; An Exploration of a Dynamic Sequence Across Diverse Number Sets: This work introduces a novel numerical sequence concept termed "Keçeci Numbers." Keçeci Numbers are a dynamic sequence generated through an iterative process, originating from a specific starting value and an increment value. In each iteration, the increment value is added to the current value, and this "added value" is recorded in the sequence. Subsequently, a division operation is attempted on this "added value," primarily using the divisors 2 and 3, with the choice of divisor depending on the one used in the previous step. If division is successful, the quotient becomes the next element in the sequence. If the division operation fails, the primality of the "added value" (or its real/scalar part for complex/quaternion numbers, or integer part for rational numbers) is checked. If it is prime, an "Augment/Shrink then Check" (ASK) rule is invoked: a type-specific unit value is added or subtracted (based on the previous ASK application), this "modified value" is recorded in the sequence, and the division operation is re-attempted on it. If division fails again, or if the number is not prime, the "added value" (or the "modified value" post-ASK) itself becomes the next element in the sequence. This mechanism is designed to be applicable across various number sets, including positive and negative real numbers, complex numbers, floating-point numbers, rational numbers, and quaternions. The increment value, ASK unit, and divisibility checks are appropriately adapted for each number type. This flexibility of Keçeci Numbers offers rich potential for studying their behavior in different numerical systems. The patterns exhibited by the sequences, their convergence/divergence properties, and potential for chaotic behavior may constitute interesting research avenues for advanced mathematical analysis and number theory applications. This study outlines the fundamental generation mechanism of Keçeci Numbers and their initial behaviors across diverse number sets.
---
## Installation / Kurulum
```bash
conda install bilgi::kececinumbers -y
pip install kececinumbers
```
https://anaconda.org/bilgi/kececinumbers
https://pypi.org/project/kececinumbers/
https://github.com/WhiteSymmetry/kececinumbers
https://zenodo.org/records/15377660
https://zenodo.org/records/
---
## Usage / Kullanım
### Example
```python
import matplotlib.pyplot as plt
import kececinumbers as kn
print("--- Interactive Test ---")
# Adım 1: get_interactive'ten tüm verileri al
# Not: Fonksiyon artık birden fazla değer döndürüyor.
interactive_results = kn.get_interactive()
# Fonksiyon bir dizi döndürdüyse (başarılıysa) devam et
if interactive_results and interactive_results[0]:
# Dönen değerleri değişkenlere ata
seq_interactive, type_choice, start_val, add_val, steps = interactive_results
# Tip numarasını isme çevirelim
type_names = [
"Positive Real", "Negative Real", "Complex", "Float", "Rational",
"Quaternion", "Neutrosophic", "Neutro-Complex", "Hyperreal",
"Bicomplex", "Neutro-Bicomplex"
]
type_name = type_names[type_choice - 1]
# Adım 2: Ayrıntılı raporu yazdır
params = {
'type_choice': type_choice,
'type_name': type_name,
'start_val': start_val,
'add_val': add_val,
'steps': steps
}
kn.print_detailed_report(seq_interactive, params)
# Adım 3: Grafiği SADECE BİR KERE çizdir
print("\nDisplaying plot...")
plot_title = f"Interactive Keçeci Sequence ({type_name})"
kn.plot_numbers(seq_interactive, plot_title)
plt.show()
else:
print("Sequence generation was cancelled or failed.")
```
```python
import matplotlib.pyplot as plt
import random
import numpy as np
import math
from fractions import Fraction
import quaternion # pip install numpy numpy-quaternion
import kececinumbers as kn
# Matplotlib grafiklerinin notebook içinde gösterilmesini sağla
%matplotlib inline
print("Trying interactive mode (will prompt for input in the console/output area)...")
interactive_sequence = kn.get_interactive()
if interactive_sequence:
kn.plot_numbers(interactive_sequence, title="Keçeci Numbers")
print("Done with examples.")
print("Keçeci Numbers Module Loaded.")
print("This module provides functions to generate and plot Keçeci Numbers.")
print("Example: Use 'import kececinumbers as kn' in your script/notebook.")
print("\nAvailable functions:")
print("- kn.get_interactive()")
print("- kn.get_with_params(kececi_type, iterations, ...)")
print("- kn.get_random_type(iterations, ...)")
print("- kn.plot_numbers(sequence, title)")
print("- kn.unified_generator(...) (low-level)")
print("\nAccess definitions with: kn.DEFINITIONS")
print("\nAccess type constants like: kn.TYPE_COMPLEX")
```
---
Trying interactive mode (will prompt for input in the console/output area)...
Keçeci Number Types:
1: Positive Real Numbers (Integer: e.g., 1)
2: Negative Real Numbers (Integer: e.g., -3)
3: Complex Numbers (e.g., 3+4j)
4: Floating-Point Numbers (e.g., 2.5)
5: Rational Numbers (e.g., 3/2, 5)
6: Quaternions (scalar start input becomes q(s,s,s,s): e.g., 1 or 2.5)
7: Neutrosophic
8: Neutro-Complex
9: Hyperreal
10: Bicomplex
11: Neutro-Bicomplex
Please select Keçeci Number Type (1-11): 1
Enter the starting number (e.g., 0 or 2.5, complex:3+4j, rational: 3/4, quaternions: 1) : 0
Enter the base scalar value for increment (e.g., 9): 9
Enter the number of iterations (positive integer: e.g., 30): 30
---
---
# Keçeci Prime Number
```python
import matplotlib.pyplot as plt
import kececinumbers as kn
print("--- Interactive Test ---")
seq_interactive = kn.get_interactive()
if seq_interactive:
kn.plot_numbers(seq_interactive, "Keçeci Numbers")
print("\n--- Random Type Test (60 Keçeci Steps) ---")
# num_iterations burada Keçeci adımı sayısıdır
seq_random = kn.get_random_type(num_iterations=60)
if seq_random:
kn.plot_numbers(seq_random, "Random Type Keçeci Numbers")
print("\n--- Fixed Params Test (Complex, 60 Keçeci Steps) ---")
seq_fixed = kn.get_with_params(
kececi_type_choice=kn.TYPE_COMPLEX,
iterations=60,
start_value_raw="1+2j",
add_value_base_scalar=3.0
)
if seq_fixed:
kn.plot_numbers(seq_fixed, "Fixed Params (Complex) Keçeci Numbers")
# İsterseniz find_kececi_prime_number'ı ayrıca da çağırabilirsiniz:
if seq_fixed:
kpn_direct = kn.find_kececi_prime_number(seq_fixed)
if kpn_direct is not None:
print(f"\nDirect call to find_kececi_prime_number for fixed numbers: {kpn_direct}")
```
Generated Keçeci Sequence (first 20 of 121): [4, 11, 12, 4, 11, 10, 5, 12, 4, 11, 12, 6, 13, 12, 4, 11, 12, 6, 13, 12]...
Keçeci Prime Number for this sequence: 11
--- Random Type Test (60 Keçeci Steps) ---
Randomly selected Keçeci Number Type: 1 (Positive Integer)
Generated Keçeci Sequence (using get_with_params, first 20 of 61): [0, 9, 3, 12, 6, 15, 5, 14, 7, 16, 8, 17, 18, 6, 15, 5, 14, 7, 16, 8]...
Keçeci Prime Number for this sequence: 17
---
## License / Lisans
This project is licensed under the MIT License. See the `LICENSE` file for details.
## Citation
If this library was useful to you in your research, please cite us. Following the [GitHub citation standards](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files), here is the recommended citation.
### BibTeX
```bibtex
@misc{kececi_2025_15377659,
author = {Keçeci, Mehmet},
title = {kececinumbers},
month = may,
year = 2025,
publisher = {PyPI, Anaconda, Github, Zenodo},
version = {0.1.0},
doi = {10.5281/zenodo.15377659},
url = {https://doi.org/10.5281/zenodo.15377659},
}
```
### APA
```
Keçeci, M. (2025). Keçeci Varsayımı: Collatz Genelleştirmesi Olarak Çoklu Cebirsel Sistemlerde Yinelemeli Dinamikler. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.16702475
Keçeci, M. (2025). Geometric Interpretations of Keçeci Numbers with Neutrosophic and Hyperreal Numbers. Zenodo. https://doi.org/10.5281/zenodo.16344232
Keçeci, M. (2025). Keçeci Sayılarının Nötrosofik ve Hipergerçek Sayılarla Geometrik Yorumlamaları. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.16343568
Keçeci, M. (2025). kececinumbers [Data set]. figshare. https://doi.org/10.6084/m9.figshare.29816414
Keçeci, M. (2025). kececinumbers [Data set]. Open Work Flow Articles (OWFAs), WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.14.2
Keçeci, M. (2025). kececinumbers. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.15377659
Keçeci, M. (2025). Keçeci Numbers and the Keçeci Prime Number: A Potential Number Theoretic Exploratory Tool. https://doi.org/10.5281/zenodo.15381698
Keçeci, M. (2025). Diversity of Keçeci Numbers and Their Application to Prešić-Type Fixed-Point Iterations: A Numerical Exploration. https://doi.org/10.5281/zenodo.15481711
Keçeci, M. (2025). Keçeci Numbers and the Keçeci Prime Number. Authorea. June 02, 2025. https://doi.org/10.22541/au.174890181.14730464/v1
Keçeci, M. (2025, May 11). Keçeci numbers and the Keçeci prime number: A potential number theoretic exploratory tool. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.15381697
```
### Chicago
```
Keçeci, Mehmet. Keçeci Varsayımı: Collatz Genelleştirmesi Olarak Çoklu Cebirsel Sistemlerde Yinelemeli Dinamikler. Open Science Articles (OSAs), Zenodo. 2025. https://doi.org/10.5281/zenodo.16702475
Keçeci, Mehmet. kececinumbers [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.14.1
Keçeci, Mehmet. "kececinumbers". Open Science Articles (OSAs), Zenodo, 01 May 2025. https://doi.org/10.5281/zenodo.15377659
Keçeci, Mehmet. "Keçeci Numbers and the Keçeci Prime Number: A Potential Number Theoretic Exploratory Tool", 11 Mayıs 2025. https://doi.org/10.5281/zenodo.15381698
Keçeci, Mehmet. "Diversity of Keçeci Numbers and Their Application to Prešić-Type Fixed-Point Iterations: A Numerical Exploration". https://doi.org/10.5281/zenodo.15481711
Keçeci, Mehmet. "Keçeci Numbers and the Keçeci Prime Number". Authorea. June 02, 2025. https://doi.org/10.22541/au.174890181.14730464/v1
Keçeci, Mehmet. Keçeci numbers and the Keçeci prime number: A potential number theoretic exploratory tool. Open Science Articles (OSAs), Zenodo. 2025. https://doi.org/10.5281/zenodo.15381697
```
---
# Keçeci Conjecture: Keçeci Varsayımı, Keçeci-Vermutung, Conjecture de Keçeci, Гипотеза Кечеджи, Keçeci Hipoteza, 凯杰西猜想, Keçeci Xiǎngcāng, ケジェジ予想, Keçeci Yosō, Keçeci Huds, Keçeci Hudsiye, Keçeci Hudsia, حدس كَچَه جِي ,حدس کچه جی ,کچہ جی حدسیہ
---
### 🇹🇷 **Türkçe**
```text
## Keçeci Varsayımı (Keçeci Conjecture) - Önerilen
Her Keçeci Sayı türü için, `unified_generator` fonksiyonu tarafından oluşturulan dizilerin, sonlu adımdan sonra periyodik bir yapıya veya tekrar eden bir asal temsiline (Keçeci Asal Sayısı, KPN) yakınsadığı sanılmaktadır. Bu davranış, Collatz Varsayımı'nın çoklu cebirsel sistemlere genişletilmiş bir hali olarak değerlendirilebilir.
Henüz kanıtlanmamıştır ve bu modül bu varsayımı test etmek için bir çerçeve sunar.
```
---
### 🇬🇧 **İngilizce (English)**
```text
## Keçeci Conjecture - Proposed
For every Keçeci Number type, sequences generated by the `unified_generator` function are conjectured to converge to a periodic structure or a recurring prime representation (Keçeci Prime Number, KPN) in finitely many steps. This behavior can be viewed as a generalization of the Collatz Conjecture to multiple algebraic systems.
It remains unproven, and this module provides a framework for testing the conjecture.
```
---
### 🇩🇪 **Almanca (Deutsch)**
```text
## Keçeci-Vermutung – Vorgeschlagen
Es wird vermutet, dass die vom `unified_generator` erzeugten Sequenzen für jeden Keçeci-Zahl-Typ nach endlich vielen Schritten gegen eine periodische Struktur oder eine wiederkehrende Primdarstellung (Keçeci-Primzahl, KPN) konvergieren. Dieses Verhalten kann als eine Erweiterung der Collatz-Vermutung auf mehrere algebraische Systeme betrachtet werden.
Die Vermutung ist bisher unbewiesen, und dieses Modul bietet einen Rahmen, um sie zu untersuchen.
```
---
### 🇫🇷 **Fransızca (Français)**
```text
## Conjecture de Keçeci – Proposée
On conjecture que, pour chaque type de nombre Keçeci, les suites générées par la fonction `unified_generator` convergent, en un nombre fini d'étapes, vers une structure périodique ou une représentation première récurrente (Nombre Premier Keçeci, KPN). Ce comportement peut être vu comme une généralisation de la conjecture de Collatz à divers systèmes algébriques.
Elle n'est pas encore démontrée, et ce module fournit un cadre pour la tester.
```
---
### 🇷🇺 **Rusça (Русский)**
```text
## Гипотеза Кечеджи — Предложенная
Предполагается, что последовательности, генерируемые функцией `unified_generator` для каждого типа чисел Кечеджи, сходятся к периодической структуре или повторяющемуся простому представлению (Простое число Кечеджи, KPN) за конечное число шагов. Это поведение можно рассматривать как обобщение гипотезы Коллатца на многомерные алгебраические системы.
Гипотеза пока не доказана, и данный модуль предоставляет среду для её проверки.
```
---
### 🇨🇳 **Çince (中文 - Basitleştirilmiş)**
```text
## 凯杰西猜想（Keçeci Conjecture）— 提出
据推测，对于每一种凯杰西数类型，由 `unified_generator` 函数生成的序列将在有限步内收敛到周期性结构或重复的素数表示（凯杰西素数，KPN）。这种行为可视为科拉茨猜想在多种代数系统中的推广。
该猜想尚未被证明，本模块提供了一个用于测试该猜想的框架。
```
---
### 🇯🇵 **Japonca (日本語)**
```text
## ケジェジ予想（Keçeci Conjecture）― 提案
すべてのケジェジ数型に対して、`unified_generator` 関数によって生成される数列は、有限回のステップ後に周期的な構造または繰り返し現れる素数表現（ケジェジ素数、KPN）に収束すると考えられている。この振る舞いは、コラッツ予想を複数の代数系へと拡張したものと見なせる。
この予想は未だ証明されておらず、本モジュールはその検証のための枠組みを提供する。
```
---
### 🇸🇦 **Arapça (العربية): "كَچَه جِي"**
```text
## حدس كَچَه جِي (Keçeci Conjecture) — مقترح
يُفترض أن المتتاليات التي يولدها الدالة `unified_generator` لكل نوع من أعداد كَچَه جِي تتقارب، بعد عدد محدود من الخطوات، إلى بنية دورية أو إلى تمثيل أولي متكرر (العدد الأولي لكَچَه جِي، KPN). يمكن اعتبار هذا السلوك تعميمًا لحدس كولاتز على نظم جبرية متعددة.
ما زال هذا الحدس غير مثبت، ويقدم هذا الوحدة إطارًا لاختباره.
```
---
### 🇮🇷 **Farsça (فارسی): "کچه جی"**
```text
## حدس کچه جی (Keçeci Conjecture) — پیشنهادی
گمان میرود که دنبالههای تولید شده توسط تابع `unified_generator` برای هر نوع از اعداد کچه جی، پس از تعداد محدودی گام، به یک ساختار تناوبی یا نمایش اول تکراری (عدد اول کچه جی، KPN) همگرا شوند. این رفتار را میتوان تعمیمی از حدس کولاتز به سیستمهای جبری چندگانه دانست.
این حدس هنوز اثبات نشده است و این ماژول چارچوبی برای آزمودن آن فراهم میکند.
```
---
### 🇵🇰 **Urduca (اردو): "کچہ جی"**
```text
## کچہ جی حدسیہ (Keçeci Conjecture) — تجویز شدہ
ہر قسم کے کچہ جی نمبر کے لیے، یہ تجویز کیا جاتا ہے کہ `unified_generator` فنکشن کے ذریعے تیار کردہ ترادف محدود مراحل کے بعد ایک دوری ساخت یا دہرائے گئے مفرد نمائندگی (کچہ جی مفرد نمبر، KPN) کی طرف مائل ہوتا ہے۔ اس رویے کو کولاتز حدسیہ کی متعدد الجبری نظاموں تک توسیع کے طور پر دیکھا جا سکتا ہے۔
ابھی تک یہ ثابت نہیں ہوا ہے، اور یہ ماڈیول اس حدسیہ کی جانچ کے لیے ایک فریم ورک فراہم کرتا ہے۔
```
Raw data
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"description": "# Ke\u00e7eci Numbers: Ke\u00e7eci Say\u0131lar\u0131\n\n[](https://badge.fury.io/py/kececinumbers)\n[](https://opensource.org/licenses/MIT)\n\n[](https://doi.org/10.5281/zenodo.15377659)\n\n[](https://doi.org/10.48546/workflowhub.datafile.14.2)\n\n[](https://doi.org/10.6084/m9.figshare.29816414)\n\n[](https://anaconda.org/bilgi/kececinumbers)\n[](https://anaconda.org/bilgi/kececinumbers)\n[](https://anaconda.org/bilgi/kececinumbers)\n[](https://anaconda.org/bilgi/kececinumbers)\n\n[](https://opensource.org/)\n[](https://kececinumbers.readthedocs.io/en/latest)\n\n[](https://www.bestpractices.dev/projects/10536)\n\n[](https://github.com/WhiteSymmetry/kececinumbers/actions/workflows/python_ci.yml)\n[](https://codecov.io/gh/WhiteSymmetry/kececinumbers)\n[](https://kececinumbers.readthedocs.io/en/latest/)\n[](https://terrarium.evidencepub.io/v2/gh/WhiteSymmetry/kececinumbers/HEAD)\n[](https://badge.fury.io/py/kececinumbers)\n[](https://pepy.tech/projects/kececinumbers)\n[](CODE_OF_CONDUCT.md)\n[](https://github.com/astral-sh/ruff)\n\n---\n\n<p align=\"left\">\n <table>\n <tr>\n <td style=\"text-align: center;\">PyPI</td>\n <td style=\"text-align: center;\">\n <a href=\"https://pypi.org/project/kececinumbers/\">\n <img src=\"https://badge.fury.io/py/kececinumbers.svg\" alt=\"PyPI version\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">Conda</td>\n <td style=\"text-align: center;\">\n <a href=\"https://anaconda.org/bilgi/kececinumbers\">\n <img src=\"https://anaconda.org/bilgi/kececinumbers/badges/version.svg\" alt=\"conda-forge version\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">DOI</td>\n <td style=\"text-align: center;\">\n <a href=\"https://doi.org/10.5281/zenodo.15377659\">\n <img src=\"https://zenodo.org/badge/DOI/10.5281/zenodo.15377659.svg\" alt=\"DOI\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">License: MIT</td>\n <td style=\"text-align: center;\">\n <a href=\"https://opensource.org/licenses/MIT\">\n <img src=\"https://img.shields.io/badge/License-MIT-yellow.svg\" alt=\"License\" height=\"18\"/>\n </a>\n </td>\n </tr>\n </table>\n</p>\n\n---\n\n## Description / A\u00e7\u0131klama\n\n**Ke\u00e7eci Numbers (Ke\u00e7eci Say\u0131lar\u0131)**: Ke\u00e7eci Numbers; An Exploration of a Dynamic Sequence Across Diverse Number Sets: This work introduces a novel numerical sequence concept termed \"Ke\u00e7eci Numbers.\" Ke\u00e7eci Numbers are a dynamic sequence generated through an iterative process, originating from a specific starting value and an increment value. In each iteration, the increment value is added to the current value, and this \"added value\" is recorded in the sequence. Subsequently, a division operation is attempted on this \"added value,\" primarily using the divisors 2 and 3, with the choice of divisor depending on the one used in the previous step. If division is successful, the quotient becomes the next element in the sequence. If the division operation fails, the primality of the \"added value\" (or its real/scalar part for complex/quaternion numbers, or integer part for rational numbers) is checked. If it is prime, an \"Augment/Shrink then Check\" (ASK) rule is invoked: a type-specific unit value is added or subtracted (based on the previous ASK application), this \"modified value\" is recorded in the sequence, and the division operation is re-attempted on it. If division fails again, or if the number is not prime, the \"added value\" (or the \"modified value\" post-ASK) itself becomes the next element in the sequence. This mechanism is designed to be applicable across various number sets, including positive and negative real numbers, complex numbers, floating-point numbers, rational numbers, and quaternions. The increment value, ASK unit, and divisibility checks are appropriately adapted for each number type. This flexibility of Ke\u00e7eci Numbers offers rich potential for studying their behavior in different numerical systems. The patterns exhibited by the sequences, their convergence/divergence properties, and potential for chaotic behavior may constitute interesting research avenues for advanced mathematical analysis and number theory applications. This study outlines the fundamental generation mechanism of Ke\u00e7eci Numbers and their initial behaviors across diverse number sets.\n\n---\n\n## Installation / Kurulum\n\n```bash\nconda install bilgi::kececinumbers -y\n\npip install kececinumbers\n```\nhttps://anaconda.org/bilgi/kececinumbers\n\nhttps://pypi.org/project/kececinumbers/\n\nhttps://github.com/WhiteSymmetry/kececinumbers\n\nhttps://zenodo.org/records/15377660\n\nhttps://zenodo.org/records/\n\n---\n\n## Usage / Kullan\u0131m\n\n### Example\n\n```python\nimport matplotlib.pyplot as plt\nimport kececinumbers as kn\n\nprint(\"--- Interactive Test ---\")\n\n# Ad\u0131m 1: get_interactive'ten t\u00fcm verileri al\n# Not: Fonksiyon art\u0131k birden fazla de\u011fer d\u00f6nd\u00fcr\u00fcyor.\ninteractive_results = kn.get_interactive()\n\n# Fonksiyon bir dizi d\u00f6nd\u00fcrd\u00fcyse (ba\u015far\u0131l\u0131ysa) devam et\nif interactive_results and interactive_results[0]:\n # D\u00f6nen de\u011ferleri de\u011fi\u015fkenlere ata\n seq_interactive, type_choice, start_val, add_val, steps = interactive_results\n \n # Tip numaras\u0131n\u0131 isme \u00e7evirelim\n type_names = [\n \"Positive Real\", \"Negative Real\", \"Complex\", \"Float\", \"Rational\", \n \"Quaternion\", \"Neutrosophic\", \"Neutro-Complex\", \"Hyperreal\", \n \"Bicomplex\", \"Neutro-Bicomplex\"\n ]\n type_name = type_names[type_choice - 1]\n\n # Ad\u0131m 2: Ayr\u0131nt\u0131l\u0131 raporu yazd\u0131r\n params = {\n 'type_choice': type_choice,\n 'type_name': type_name,\n 'start_val': start_val,\n 'add_val': add_val,\n 'steps': steps\n }\n kn.print_detailed_report(seq_interactive, params)\n \n # Ad\u0131m 3: Grafi\u011fi SADECE B\u0130R KERE \u00e7izdir\n print(\"\\nDisplaying plot...\")\n plot_title = f\"Interactive Ke\u00e7eci Sequence ({type_name})\"\n kn.plot_numbers(seq_interactive, plot_title)\n plt.show()\n\nelse:\n print(\"Sequence generation was cancelled or failed.\")\n```\n\n```python\nimport matplotlib.pyplot as plt\nimport random\nimport numpy as np\nimport math\nfrom fractions import Fraction\nimport quaternion # pip install numpy numpy-quaternion\nimport kececinumbers as kn\n\n# Matplotlib grafiklerinin notebook i\u00e7inde g\u00f6sterilmesini sa\u011fla\n%matplotlib inline\n\nprint(\"Trying interactive mode (will prompt for input in the console/output area)...\")\ninteractive_sequence = kn.get_interactive()\nif interactive_sequence:\n kn.plot_numbers(interactive_sequence, title=\"Ke\u00e7eci Numbers\")\n\nprint(\"Done with examples.\")\nprint(\"Ke\u00e7eci Numbers Module Loaded.\")\nprint(\"This module provides functions to generate and plot Ke\u00e7eci Numbers.\")\nprint(\"Example: Use 'import kececinumbers as kn' in your script/notebook.\")\nprint(\"\\nAvailable functions:\")\nprint(\"- kn.get_interactive()\")\nprint(\"- kn.get_with_params(kececi_type, iterations, ...)\")\nprint(\"- kn.get_random_type(iterations, ...)\")\nprint(\"- kn.plot_numbers(sequence, title)\")\nprint(\"- kn.unified_generator(...) (low-level)\")\nprint(\"\\nAccess definitions with: kn.DEFINITIONS\")\nprint(\"\\nAccess type constants like: kn.TYPE_COMPLEX\")\n```\n---\nTrying interactive mode (will prompt for input in the console/output area)...\n\nKe\u00e7eci Number Types:\n\n1: Positive Real Numbers (Integer: e.g., 1)\n\n2: Negative Real Numbers (Integer: e.g., -3)\n\n3: Complex Numbers (e.g., 3+4j)\n\n4: Floating-Point Numbers (e.g., 2.5)\n\n5: Rational Numbers (e.g., 3/2, 5)\n\n6: Quaternions (scalar start input becomes q(s,s,s,s): e.g., 1 or 2.5)\n\n7: Neutrosophic \n\n8: Neutro-Complex \n\n9: Hyperreal\n \n10: Bicomplex \n\n11: Neutro-Bicomplex\n\nPlease select Ke\u00e7eci Number Type (1-11): 1\n\nEnter the starting number (e.g., 0 or 2.5, complex:3+4j, rational: 3/4, quaternions: 1) : 0\n\nEnter the base scalar value for increment (e.g., 9): 9\n\nEnter the number of iterations (positive integer: e.g., 30): 30\n\n---\n\n\n\n\n\n\n\n\n\n\n---\n# Ke\u00e7eci Prime Number\n\n```python\nimport matplotlib.pyplot as plt\nimport kececinumbers as kn\n\n\nprint(\"--- Interactive Test ---\")\nseq_interactive = kn.get_interactive()\nif seq_interactive:\n kn.plot_numbers(seq_interactive, \"Ke\u00e7eci Numbers\")\n\nprint(\"\\n--- Random Type Test (60 Ke\u00e7eci Steps) ---\")\n# num_iterations burada Ke\u00e7eci ad\u0131m\u0131 say\u0131s\u0131d\u0131r\nseq_random = kn.get_random_type(num_iterations=60) \nif seq_random:\n kn.plot_numbers(seq_random, \"Random Type Ke\u00e7eci Numbers\")\n\nprint(\"\\n--- Fixed Params Test (Complex, 60 Ke\u00e7eci Steps) ---\")\nseq_fixed = kn.get_with_params(\n kececi_type_choice=kn.TYPE_COMPLEX, \n iterations=60, \n start_value_raw=\"1+2j\", \n add_value_base_scalar=3.0\n)\nif seq_fixed:\n kn.plot_numbers(seq_fixed, \"Fixed Params (Complex) Ke\u00e7eci Numbers\")\n\n# \u0130sterseniz find_kececi_prime_number'\u0131 ayr\u0131ca da \u00e7a\u011f\u0131rabilirsiniz:\nif seq_fixed:\n kpn_direct = kn.find_kececi_prime_number(seq_fixed)\n if kpn_direct is not None:\n print(f\"\\nDirect call to find_kececi_prime_number for fixed numbers: {kpn_direct}\")\n```\n\nGenerated Ke\u00e7eci Sequence (first 20 of 121): [4, 11, 12, 4, 11, 10, 5, 12, 4, 11, 12, 6, 13, 12, 4, 11, 12, 6, 13, 12]...\nKe\u00e7eci Prime Number for this sequence: 11\n\n--- Random Type Test (60 Ke\u00e7eci Steps) ---\n\nRandomly selected Ke\u00e7eci Number Type: 1 (Positive Integer)\n\nGenerated Ke\u00e7eci Sequence (using get_with_params, first 20 of 61): [0, 9, 3, 12, 6, 15, 5, 14, 7, 16, 8, 17, 18, 6, 15, 5, 14, 7, 16, 8]...\nKe\u00e7eci Prime Number for this sequence: 17\n\n---\n\n## License / Lisans\n\nThis project is licensed under the MIT License. See the `LICENSE` file for details.\n\n## Citation\n\nIf this library was useful to you in your research, please cite us. Following the [GitHub citation standards](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files), here is the recommended citation.\n\n### BibTeX\n\n```bibtex\n@misc{kececi_2025_15377659,\n author = {Ke\u00e7eci, Mehmet},\n title = {kececinumbers},\n month = may,\n year = 2025,\n publisher = {PyPI, Anaconda, Github, Zenodo},\n version = {0.1.0},\n doi = {10.5281/zenodo.15377659},\n url = {https://doi.org/10.5281/zenodo.15377659},\n}\n```\n\n### APA\n\n```\n\nKe\u00e7eci, M. (2025). Ke\u00e7eci Varsay\u0131m\u0131: Collatz Genelle\u015ftirmesi Olarak \u00c7oklu Cebirsel Sistemlerde Yinelemeli Dinamikler. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.16702475\n\nKe\u00e7eci, M. (2025). Geometric Interpretations of Ke\u00e7eci Numbers with Neutrosophic and Hyperreal Numbers. Zenodo. https://doi.org/10.5281/zenodo.16344232\n\nKe\u00e7eci, M. (2025). Ke\u00e7eci Say\u0131lar\u0131n\u0131n N\u00f6trosofik ve Hiperger\u00e7ek Say\u0131larla Geometrik Yorumlamalar\u0131. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.16343568\n\nKe\u00e7eci, M. (2025). kececinumbers [Data set]. figshare. https://doi.org/10.6084/m9.figshare.29816414\n\nKe\u00e7eci, M. (2025). kececinumbers [Data set]. Open Work Flow Articles (OWFAs), WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.14.2\n\nKe\u00e7eci, M. (2025). kececinumbers. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.15377659\n\nKe\u00e7eci, M. (2025). Ke\u00e7eci Numbers and the Ke\u00e7eci Prime Number: A Potential Number Theoretic Exploratory Tool. https://doi.org/10.5281/zenodo.15381698\n\nKe\u00e7eci, M. (2025). Diversity of Ke\u00e7eci Numbers and Their Application to Pre\u0161i\u0107-Type Fixed-Point Iterations: A Numerical Exploration. https://doi.org/10.5281/zenodo.15481711\n\nKe\u00e7eci, M. (2025). Ke\u00e7eci Numbers and the Ke\u00e7eci Prime Number. Authorea. June 02, 2025. https://doi.org/10.22541/au.174890181.14730464/v1\n\nKe\u00e7eci, M. (2025, May 11). Ke\u00e7eci numbers and the Ke\u00e7eci prime number: A potential number theoretic exploratory tool. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.15381697\n```\n\n### Chicago\n```\n\nKe\u00e7eci, Mehmet. Ke\u00e7eci Varsay\u0131m\u0131: Collatz Genelle\u015ftirmesi Olarak \u00c7oklu Cebirsel Sistemlerde Yinelemeli Dinamikler. Open Science Articles (OSAs), Zenodo. 2025. https://doi.org/10.5281/zenodo.16702475\n\nKe\u00e7eci, Mehmet. kececinumbers [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.14.1\n\nKe\u00e7eci, Mehmet. \"kececinumbers\". Open Science Articles (OSAs), Zenodo, 01 May 2025. https://doi.org/10.5281/zenodo.15377659\n\nKe\u00e7eci, Mehmet. \"Ke\u00e7eci Numbers and the Ke\u00e7eci Prime Number: A Potential Number Theoretic Exploratory Tool\", 11 May\u0131s 2025. https://doi.org/10.5281/zenodo.15381698\n\nKe\u00e7eci, Mehmet. \"Diversity of Ke\u00e7eci Numbers and Their Application to Pre\u0161i\u0107-Type Fixed-Point Iterations: A Numerical Exploration\". https://doi.org/10.5281/zenodo.15481711\n\nKe\u00e7eci, Mehmet. \"Ke\u00e7eci Numbers and the Ke\u00e7eci Prime Number\". Authorea. June 02, 2025. https://doi.org/10.22541/au.174890181.14730464/v1\n\nKe\u00e7eci, Mehmet. Ke\u00e7eci numbers and the Ke\u00e7eci prime number: A potential number theoretic exploratory tool. Open Science Articles (OSAs), Zenodo. 2025. https://doi.org/10.5281/zenodo.15381697\n```\n\n---\n\n# Ke\u00e7eci Conjecture: Ke\u00e7eci Varsay\u0131m\u0131, Ke\u00e7eci-Vermutung, Conjecture de Ke\u00e7eci, \u0413\u0438\u043f\u043e\u0442\u0435\u0437\u0430 \u041a\u0435\u0447\u0435\u0434\u0436\u0438, Ke\u00e7eci Hipoteza, \u51ef\u6770\u897f\u731c\u60f3, Ke\u00e7eci Xi\u01cengc\u0101ng, \u30b1\u30b8\u30a7\u30b8\u4e88\u60f3, Ke\u00e7eci Yos\u014d, Ke\u00e7eci Huds, Ke\u00e7eci Hudsiye, Ke\u00e7eci Hudsia, \u062d\u062f\u0633 \u0643\u064e\u0686\u064e\u0647 \u062c\u0650\u064a ,\u062d\u062f\u0633 \u06a9\u0686\u0647 \u062c\u06cc ,\u06a9\u0686\u06c1 \u062c\u06cc \u062d\u062f\u0633\u06cc\u06c1\n---\n\n### \ud83c\uddf9\ud83c\uddf7 **T\u00fcrk\u00e7e** \n```text\n## Ke\u00e7eci Varsay\u0131m\u0131 (Ke\u00e7eci Conjecture) - \u00d6nerilen\n\nHer Ke\u00e7eci Say\u0131 t\u00fcr\u00fc i\u00e7in, `unified_generator` fonksiyonu taraf\u0131ndan olu\u015fturulan dizilerin, sonlu ad\u0131mdan sonra periyodik bir yap\u0131ya veya tekrar eden bir asal temsiline (Ke\u00e7eci Asal Say\u0131s\u0131, KPN) yak\u0131nsad\u0131\u011f\u0131 san\u0131lmaktad\u0131r. Bu davran\u0131\u015f, Collatz Varsay\u0131m\u0131'n\u0131n \u00e7oklu cebirsel sistemlere geni\u015fletilmi\u015f bir hali olarak de\u011ferlendirilebilir.\n\nHen\u00fcz kan\u0131tlanmam\u0131\u015ft\u0131r ve bu mod\u00fcl bu varsay\u0131m\u0131 test etmek i\u00e7in bir \u00e7er\u00e7eve sunar.\n```\n\n---\n\n### \ud83c\uddec\ud83c\udde7 **\u0130ngilizce (English)** \n```text\n## Ke\u00e7eci Conjecture - Proposed\n\nFor every Ke\u00e7eci Number type, sequences generated by the `unified_generator` function are conjectured to converge to a periodic structure or a recurring prime representation (Ke\u00e7eci Prime Number, KPN) in finitely many steps. This behavior can be viewed as a generalization of the Collatz Conjecture to multiple algebraic systems.\n\nIt remains unproven, and this module provides a framework for testing the conjecture.\n```\n\n---\n\n### \ud83c\udde9\ud83c\uddea **Almanca (Deutsch)** \n```text\n## Ke\u00e7eci-Vermutung \u2013 Vorgeschlagen\n\nEs wird vermutet, dass die vom `unified_generator` erzeugten Sequenzen f\u00fcr jeden Ke\u00e7eci-Zahl-Typ nach endlich vielen Schritten gegen eine periodische Struktur oder eine wiederkehrende Primdarstellung (Ke\u00e7eci-Primzahl, KPN) konvergieren. Dieses Verhalten kann als eine Erweiterung der Collatz-Vermutung auf mehrere algebraische Systeme betrachtet werden.\n\nDie Vermutung ist bisher unbewiesen, und dieses Modul bietet einen Rahmen, um sie zu untersuchen.\n```\n\n---\n\n### \ud83c\uddeb\ud83c\uddf7 **Frans\u0131zca (Fran\u00e7ais)** \n```text\n## Conjecture de Ke\u00e7eci \u2013 Propos\u00e9e\n\nOn conjecture que, pour chaque type de nombre Ke\u00e7eci, les suites g\u00e9n\u00e9r\u00e9es par la fonction `unified_generator` convergent, en un nombre fini d'\u00e9tapes, vers une structure p\u00e9riodique ou une repr\u00e9sentation premi\u00e8re r\u00e9currente (Nombre Premier Ke\u00e7eci, KPN). Ce comportement peut \u00eatre vu comme une g\u00e9n\u00e9ralisation de la conjecture de Collatz \u00e0 divers syst\u00e8mes alg\u00e9briques.\n\nElle n'est pas encore d\u00e9montr\u00e9e, et ce module fournit un cadre pour la tester.\n```\n\n\n---\n\n### \ud83c\uddf7\ud83c\uddfa **Rus\u00e7a (\u0420\u0443\u0441\u0441\u043a\u0438\u0439)** \n```text\n## \u0413\u0438\u043f\u043e\u0442\u0435\u0437\u0430 \u041a\u0435\u0447\u0435\u0434\u0436\u0438 \u2014 \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043d\u0430\u044f\n\n\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438, \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u043c\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 `unified_generator` \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0447\u0438\u0441\u0435\u043b \u041a\u0435\u0447\u0435\u0434\u0436\u0438, \u0441\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043a \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0435 \u0438\u043b\u0438 \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u044e\u0449\u0435\u043c\u0443\u0441\u044f \u043f\u0440\u043e\u0441\u0442\u043e\u043c\u0443 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044e (\u041f\u0440\u043e\u0441\u0442\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u041a\u0435\u0447\u0435\u0434\u0436\u0438, KPN) \u0437\u0430 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0448\u0430\u0433\u043e\u0432. \u042d\u0442\u043e \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044c \u043a\u0430\u043a \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u043e\u0442\u0435\u0437\u044b \u041a\u043e\u043b\u043b\u0430\u0442\u0446\u0430 \u043d\u0430 \u043c\u043d\u043e\u0433\u043e\u043c\u0435\u0440\u043d\u044b\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b.\n\n\u0413\u0438\u043f\u043e\u0442\u0435\u0437\u0430 \u043f\u043e\u043a\u0430 \u043d\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0430, \u0438 \u0434\u0430\u043d\u043d\u044b\u0439 \u043c\u043e\u0434\u0443\u043b\u044c \u043f\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u0440\u0435\u0434\u0443 \u0434\u043b\u044f \u0435\u0451 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0438.\n```\n\n---\n\n### \ud83c\udde8\ud83c\uddf3 **\u00c7ince (\u4e2d\u6587 - Basitle\u015ftirilmi\u015f)** \n```text\n## \u51ef\u6770\u897f\u731c\u60f3\uff08Ke\u00e7eci Conjecture\uff09\u2014 \u63d0\u51fa\n\n\u636e\u63a8\u6d4b\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u79cd\u51ef\u6770\u897f\u6570\u7c7b\u578b\uff0c\u7531 `unified_generator` \u51fd\u6570\u751f\u6210\u7684\u5e8f\u5217\u5c06\u5728\u6709\u9650\u6b65\u5185\u6536\u655b\u5230\u5468\u671f\u6027\u7ed3\u6784\u6216\u91cd\u590d\u7684\u7d20\u6570\u8868\u793a\uff08\u51ef\u6770\u897f\u7d20\u6570\uff0cKPN\uff09\u3002\u8fd9\u79cd\u884c\u4e3a\u53ef\u89c6\u4e3a\u79d1\u62c9\u8328\u731c\u60f3\u5728\u591a\u79cd\u4ee3\u6570\u7cfb\u7edf\u4e2d\u7684\u63a8\u5e7f\u3002\n\n\u8be5\u731c\u60f3\u5c1a\u672a\u88ab\u8bc1\u660e\uff0c\u672c\u6a21\u5757\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7528\u4e8e\u6d4b\u8bd5\u8be5\u731c\u60f3\u7684\u6846\u67b6\u3002\n```\n\n---\n\n### \ud83c\uddef\ud83c\uddf5 **Japonca (\u65e5\u672c\u8a9e)** \n```text\n## \u30b1\u30b8\u30a7\u30b8\u4e88\u60f3\uff08Ke\u00e7eci Conjecture\uff09\u2015 \u63d0\u6848\n\n\u3059\u3079\u3066\u306e\u30b1\u30b8\u30a7\u30b8\u6570\u578b\u306b\u5bfe\u3057\u3066\u3001`unified_generator` \u95a2\u6570\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b\u6570\u5217\u306f\u3001\u6709\u9650\u56de\u306e\u30b9\u30c6\u30c3\u30d7\u5f8c\u306b\u5468\u671f\u7684\u306a\u69cb\u9020\u307e\u305f\u306f\u7e70\u308a\u8fd4\u3057\u73fe\u308c\u308b\u7d20\u6570\u8868\u73fe\uff08\u30b1\u30b8\u30a7\u30b8\u7d20\u6570\u3001KPN\uff09\u306b\u53ce\u675f\u3059\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u308b\u3002\u3053\u306e\u632f\u308b\u821e\u3044\u306f\u3001\u30b3\u30e9\u30c3\u30c4\u4e88\u60f3\u3092\u8907\u6570\u306e\u4ee3\u6570\u7cfb\u3078\u3068\u62e1\u5f35\u3057\u305f\u3082\u306e\u3068\u898b\u306a\u305b\u308b\u3002\n\n\u3053\u306e\u4e88\u60f3\u306f\u672a\u3060\u8a3c\u660e\u3055\u308c\u3066\u304a\u3089\u305a\u3001\u672c\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u305d\u306e\u691c\u8a3c\u306e\u305f\u3081\u306e\u67a0\u7d44\u307f\u3092\u63d0\u4f9b\u3059\u308b\u3002\n```\n\n---\n\n### \ud83c\uddf8\ud83c\udde6 **Arap\u00e7a (\u0627\u0644\u0639\u0631\u0628\u064a\u0629): \"\u0643\u064e\u0686\u064e\u0647 \u062c\u0650\u064a\"**\n```text\n## \u062d\u062f\u0633 \u0643\u064e\u0686\u064e\u0647 \u062c\u0650\u064a (Ke\u00e7eci Conjecture) \u2014 \u0645\u0642\u062a\u0631\u062d\n\n\u064a\u064f\u0641\u062a\u0631\u0636 \u0623\u0646 \u0627\u0644\u0645\u062a\u062a\u0627\u0644\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0648\u0644\u062f\u0647\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 `unified_generator` \u0644\u0643\u0644 \u0646\u0648\u0639 \u0645\u0646 \u0623\u0639\u062f\u0627\u062f \u0643\u064e\u0686\u064e\u0647 \u062c\u0650\u064a \u062a\u062a\u0642\u0627\u0631\u0628\u060c \u0628\u0639\u062f \u0639\u062f\u062f \u0645\u062d\u062f\u0648\u062f \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a\u060c \u0625\u0644\u0649 \u0628\u0646\u064a\u0629 \u062f\u0648\u0631\u064a\u0629 \u0623\u0648 \u0625\u0644\u0649 \u062a\u0645\u062b\u064a\u0644 \u0623\u0648\u0644\u064a \u0645\u062a\u0643\u0631\u0631 (\u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0648\u0644\u064a \u0644\u0643\u064e\u0686\u064e\u0647 \u062c\u0650\u064a\u060c KPN). \u064a\u0645\u0643\u0646 \u0627\u0639\u062a\u0628\u0627\u0631 \u0647\u0630\u0627 \u0627\u0644\u0633\u0644\u0648\u0643 \u062a\u0639\u0645\u064a\u0645\u064b\u0627 \u0644\u062d\u062f\u0633 \u0643\u0648\u0644\u0627\u062a\u0632 \u0639\u0644\u0649 \u0646\u0638\u0645 \u062c\u0628\u0631\u064a\u0629 \u0645\u062a\u0639\u062f\u062f\u0629.\n\n\u0645\u0627 \u0632\u0627\u0644 \u0647\u0630\u0627 \u0627\u0644\u062d\u062f\u0633 \u063a\u064a\u0631 \u0645\u062b\u0628\u062a\u060c \u0648\u064a\u0642\u062f\u0645 \u0647\u0630\u0627 \u0627\u0644\u0648\u062d\u062f\u0629 \u0625\u0637\u0627\u0631\u064b\u0627 \u0644\u0627\u062e\u062a\u0628\u0627\u0631\u0647.\n```\n\n---\n\n### \ud83c\uddee\ud83c\uddf7 **Fars\u00e7a (\u0641\u0627\u0631\u0633\u06cc): \"\u06a9\u0686\u0647 \u062c\u06cc\"**\n```text\n## \u062d\u062f\u0633 \u06a9\u0686\u0647 \u062c\u06cc (Ke\u00e7eci Conjecture) \u2014 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f\u06cc\n\n\u06af\u0645\u0627\u0646 \u0645\u06cc\u200c\u0631\u0648\u062f \u06a9\u0647 \u062f\u0646\u0628\u0627\u0644\u0647\u200c\u0647\u0627\u06cc \u062a\u0648\u0644\u06cc\u062f \u0634\u062f\u0647 \u062a\u0648\u0633\u0637 \u062a\u0627\u0628\u0639 `unified_generator` \u0628\u0631\u0627\u06cc \u0647\u0631 \u0646\u0648\u0639 \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u06a9\u0686\u0647 \u062c\u06cc\u060c \u067e\u0633 \u0627\u0632 \u062a\u0639\u062f\u0627\u062f \u0645\u062d\u062f\u0648\u062f\u06cc \u06af\u0627\u0645\u060c \u0628\u0647 \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u062a\u0646\u0627\u0648\u0628\u06cc \u06cc\u0627 \u0646\u0645\u0627\u06cc\u0634 \u0627\u0648\u0644 \u062a\u06a9\u0631\u0627\u0631\u06cc (\u0639\u062f\u062f \u0627\u0648\u0644 \u06a9\u0686\u0647 \u062c\u06cc\u060c KPN) \u0647\u0645\u06af\u0631\u0627 \u0634\u0648\u0646\u062f. \u0627\u06cc\u0646 \u0631\u0641\u062a\u0627\u0631 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062a\u0639\u0645\u06cc\u0645\u06cc \u0627\u0632 \u062d\u062f\u0633 \u06a9\u0648\u0644\u0627\u062a\u0632 \u0628\u0647 \u0633\u06cc\u0633\u062a\u0645\u200c\u0647\u0627\u06cc \u062c\u0628\u0631\u06cc \u0686\u0646\u062f\u06af\u0627\u0646\u0647 \u062f\u0627\u0646\u0633\u062a.\n\n\u0627\u06cc\u0646 \u062d\u062f\u0633 \u0647\u0646\u0648\u0632 \u0627\u062b\u0628\u0627\u062a \u0646\u0634\u062f\u0647 \u0627\u0633\u062a \u0648 \u0627\u06cc\u0646 \u0645\u0627\u0698\u0648\u0644 \u0686\u0627\u0631\u0686\u0648\u0628\u06cc \u0628\u0631\u0627\u06cc \u0622\u0632\u0645\u0648\u062f\u0646 \u0622\u0646 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f.\n```\n\n---\n\n### \ud83c\uddf5\ud83c\uddf0 **Urduca (\u0627\u0631\u062f\u0648): \"\u06a9\u0686\u06c1 \u062c\u06cc\"**\n```text\n## \u06a9\u0686\u06c1 \u062c\u06cc \u062d\u062f\u0633\u06cc\u06c1 (Ke\u00e7eci Conjecture) \u2014 \u062a\u062c\u0648\u06cc\u0632 \u0634\u062f\u06c1\n\n\u06c1\u0631 \u0642\u0633\u0645 \u06a9\u06d2 \u06a9\u0686\u06c1 \u062c\u06cc \u0646\u0645\u0628\u0631 \u06a9\u06d2 \u0644\u06cc\u06d2\u060c \u06cc\u06c1 \u062a\u062c\u0648\u06cc\u0632 \u06a9\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2 \u06a9\u06c1 `unified_generator` \u0641\u0646\u06a9\u0634\u0646 \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06d2 \u062a\u06cc\u0627\u0631 \u06a9\u0631\u062f\u06c1 \u062a\u0631\u0627\u062f\u0641 \u0645\u062d\u062f\u0648\u062f \u0645\u0631\u0627\u062d\u0644 \u06a9\u06d2 \u0628\u0639\u062f \u0627\u06cc\u06a9 \u062f\u0648\u0631\u06cc \u0633\u0627\u062e\u062a \u06cc\u0627 \u062f\u06c1\u0631\u0627\u0626\u06d2 \u06af\u0626\u06d2 \u0645\u0641\u0631\u062f \u0646\u0645\u0627\u0626\u0646\u062f\u06af\u06cc (\u06a9\u0686\u06c1 \u062c\u06cc \u0645\u0641\u0631\u062f \u0646\u0645\u0628\u0631\u060c KPN) \u06a9\u06cc \u0637\u0631\u0641 \u0645\u0627\u0626\u0644 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4 \u0627\u0633 \u0631\u0648\u06cc\u06d2 \u06a9\u0648 \u06a9\u0648\u0644\u0627\u062a\u0632 \u062d\u062f\u0633\u06cc\u06c1 \u06a9\u06cc \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062c\u0628\u0631\u06cc \u0646\u0638\u0627\u0645\u0648\u06ba \u062a\u06a9 \u062a\u0648\u0633\u06cc\u0639 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u062f\u06cc\u06a9\u06be\u0627 \u062c\u0627 \u0633\u06a9\u062a\u0627 \u06c1\u06d2\u06d4\n\n\u0627\u0628\u06be\u06cc \u062a\u06a9 \u06cc\u06c1 \u062b\u0627\u0628\u062a \u0646\u06c1\u06cc\u06ba \u06c1\u0648\u0627 \u06c1\u06d2\u060c \u0627\u0648\u0631 \u06cc\u06c1 \u0645\u0627\u0688\u06cc\u0648\u0644 \u0627\u0633 \u062d\u062f\u0633\u06cc\u06c1 \u06a9\u06cc \u062c\u0627\u0646\u0686 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0627\u06cc\u06a9 \u0641\u0631\u06cc\u0645 \u0648\u0631\u06a9 \u0641\u0631\u0627\u06c1\u0645 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4\n```\n\n\n",
"bugtrack_url": null,
"license": "MIT",
"summary": "Ke\u00e7eci Numbers: An Exploration of a Dynamic Sequence Across Diverse Number Sets",
"version": "0.3.4",
"project_urls": {
"Homepage": "https://github.com/WhiteSymmetry/kececinumbers"
},
"split_keywords": [],
"urls": [
{
"comment_text": null,
"digests": {
"blake2b_256": "accdace8eaea1ba6bbfaf19aaef83c94cfd5d566df306caf0fb199303acf3085",
"md5": "daa4799dac1394315845e1a0cc3f0043",
"sha256": "e57e9374ef2dbed082d5a97946c591f22373b9191d8d7b716b2969a1b0e1b681"
},
"downloads": -1,
"filename": "kececinumbers-0.3.4-py3-none-any.whl",
"has_sig": false,
"md5_digest": "daa4799dac1394315845e1a0cc3f0043",
"packagetype": "bdist_wheel",
"python_version": "py3",
"requires_python": ">=3.9",
"size": 21199,
"upload_time": "2025-08-05T08:24:11",
"upload_time_iso_8601": "2025-08-05T08:24:11.556340Z",
"url": "https://files.pythonhosted.org/packages/ac/cd/ace8eaea1ba6bbfaf19aaef83c94cfd5d566df306caf0fb199303acf3085/kececinumbers-0.3.4-py3-none-any.whl",
"yanked": false,
"yanked_reason": null
},
{
"comment_text": null,
"digests": {
"blake2b_256": "30b986c8fa995dd18cc27987fabd72bd526ade3ee28b220ecb83947d52a58bb9",
"md5": "998e25309bf3017e15370e0ac421f80a",
"sha256": "c183fe76594e8a85fb63df3c6b44f6255d67ef7a6f58b921610bfa18dda288dd"
},
"downloads": -1,
"filename": "kececinumbers-0.3.4.tar.gz",
"has_sig": false,
"md5_digest": "998e25309bf3017e15370e0ac421f80a",
"packagetype": "sdist",
"python_version": "source",
"requires_python": ">=3.9",
"size": 28451,
"upload_time": "2025-08-05T08:24:12",
"upload_time_iso_8601": "2025-08-05T08:24:12.970118Z",
"url": "https://files.pythonhosted.org/packages/30/b9/86c8fa995dd18cc27987fabd72bd526ade3ee28b220ecb83947d52a58bb9/kececinumbers-0.3.4.tar.gz",
"yanked": false,
"yanked_reason": null
}
],
"upload_time": "2025-08-05 08:24:12",
"github": true,
"gitlab": false,
"bitbucket": false,
"codeberg": false,
"github_user": "WhiteSymmetry",
"github_project": "kececinumbers",
"travis_ci": false,
"coveralls": false,
"github_actions": true,
"requirements": [],
"lcname": "kececinumbers"
}
JSON
