110 lines
2.6 KiB
Plaintext
110 lines
2.6 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "de629cc8",
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"metadata": {},
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"source": [
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"# [Lychrel Numbers](https://projecteuler.net/problem=55)\n",
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"\n",
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"This could get tricky if we were working with fixed size integers, since the reverse-and-add process for [Lychrel numbers](https://en.wikipedia.org/wiki/Lychrel_number) can result in some big numbers. But Python ints have unlimited precision, so no need to worry about that."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "5588d5d2",
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"metadata": {},
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"outputs": [],
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"source": [
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"def is_palindrome(n):\n",
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" s = str(n)\n",
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" return s == s[::-1]\n",
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"\n",
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"\n",
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"def is_lychrel_number(n):\n",
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" for _ in range(0, 50):\n",
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" rev = int(str(n)[::-1])\n",
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" n += rev\n",
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" if is_palindrome(n):\n",
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" return False\n",
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" \n",
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" return True"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d45f3460",
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"metadata": {},
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"source": [
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"This is easy to brute force, since we're not checking that many numbers, and we loop at most 50 times in our test."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "e473996a",
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"metadata": {},
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"outputs": [],
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"source": [
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"lychrel_numbers = {n for n in range(1, 10000) if is_lychrel_number(n)}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "2c3f1cbf",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"249"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"len(lychrel_numbers)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ef8a3b03",
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"metadata": {},
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"source": [
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"## Relevant sequences\n",
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"* Suspected Lychrel numbers: [A023108](https://oeis.org/A023108)\n",
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"\n",
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"#### Copyright (C) 2025 filifa\n",
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"\n",
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"This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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