96 lines
2.3 KiB
Plaintext
96 lines
2.3 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "1899e933",
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"metadata": {},
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"source": [
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"# [Even Fibonacci Numbers](https://projecteuler.net/problem=2)\n",
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"\n",
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"There's a lot to learn about the [Fibonacci numbers](https://en.wikipedia.org/wiki/Fibonacci_sequence), and this will not be the last time we see them in a Project Euler problem, but for now this problem keeps it relatively simple.\n",
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"\n",
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"Since this is a SageMath notebook, we'll use its functionality so we can keep our code simple like the problem."
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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": "57b68465",
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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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"4613732"
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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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"sum(n for n in fibonacci_xrange(1, 4000000) if n % 2 == 0)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "eef788da",
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"metadata": {},
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"source": [
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"Even without SageMath, it's easy to implement our own generator of the sequence up to $n$."
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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": 2,
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"id": "24a7c257",
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"metadata": {},
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"outputs": [],
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"source": [
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"def fib(n):\n",
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" a = 0\n",
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" b = 1\n",
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" while a <= n:\n",
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" yield a\n",
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" a, b = b, a + b"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b3293a7d",
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"metadata": {},
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"source": [
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"## Relevant sequences\n",
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"* Fibonacci numbers: [A000045](https://oeis.org/A000045)\n",
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"* Partial sums of even Fibonacci numbers: [A099919](https://oeis.org/A099919)\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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