101 lines
2.0 KiB
Plaintext
101 lines
2.0 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Euler Problem 25\n",
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"\n",
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"The Fibonacci sequence is defined by the recurrence relation:\n",
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"\n",
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"$F_n = F_{n−1} + F_{n−2}$, where $F_1 = 1$ and $F_2 = 1$.\n",
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"Hence the first 12 terms will be:\n",
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"\n",
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"~~~\n",
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"F1 = 1\n",
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"F2 = 1\n",
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"F3 = 2\n",
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"F4 = 3\n",
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"F5 = 5\n",
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"F6 = 8\n",
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"F7 = 13\n",
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"F8 = 21\n",
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"F9 = 34\n",
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"F10 = 55\n",
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"F11 = 89\n",
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"F12 = 144\n",
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"~~~\n",
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"\n",
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"The 12th term, $F_{12}$, is the first term to contain three digits.\n",
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"\n",
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"What is the index of the first term in the Fibonacci sequence to contain 1000 digits?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Reuse fibonacci generator and then straight forward."
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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": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"4782\n"
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]
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}
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],
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"source": [
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"def fibonacci_generator():\n",
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" a = 0\n",
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" b = 1\n",
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" yield 1\n",
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" while True:\n",
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" yield a + b\n",
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" a, b = b, (a + b)\n",
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" \n",
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"for i, f in enumerate(fibonacci_generator()):\n",
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" if len(str(f)) >= 1000:\n",
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" break\n",
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"\n",
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"s = i + 1\n",
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"assert(s == 4782)\n",
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"print(s)"
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]
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}
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],
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"metadata": {
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"completion_date": "Fri, 5 Sep 2014, 14:57",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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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": "3.5.4"
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},
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"tags": [
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"fibonacci"
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]
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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