113 lines
2.6 KiB
Plaintext
113 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": "950160e4",
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"metadata": {},
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"source": [
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"# [Double-base Palindromes](https://projecteuler.net/problem=36)\n",
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"\n",
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"Python's `bin` function converts an integer to a string representing the number in binary, starting with `0b`, so we'll just slice that off before we reverse and check if it's a [palindrome](https://en.wikipedia.org/wiki/Palindromic_number)."
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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": "39bf1e12",
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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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"{1,\n",
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" 3,\n",
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" 5,\n",
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" 7,\n",
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" 9,\n",
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" 33,\n",
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" 99,\n",
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" 313,\n",
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" 585,\n",
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" 717,\n",
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" 7447,\n",
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" 9009,\n",
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" 15351,\n",
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" 32223,\n",
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" 39993,\n",
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" 53235,\n",
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" 53835,\n",
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" 73737,\n",
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" 585585}"
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]
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},
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"execution_count": 1,
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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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"is_base_2_palindrome = lambda x: bin(x)[2:] == bin(x)[:1:-1]\n",
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"is_base_10_palindrome = lambda x: str(x) == str(x)[::-1]\n",
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"\n",
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"double_palindromes = {n for n in range(1, 1000000) if is_base_2_palindrome(n) and is_base_10_palindrome(n)}\n",
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"double_palindromes"
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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": "ce61e551",
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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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"872187"
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]
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},
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"execution_count": 2,
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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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"sum(double_palindromes)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b83cbc0d",
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"metadata": {},
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"source": [
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"## Relevant sequences\n",
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"* Numbers that are base-2 and base-10 palindromes: [A007632](https://oeis.org/A007632)\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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