move notebooks to subdir

notebooks/problem0002.ipynb

@@ -0,0 +1,91 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "1899e933",
+   "metadata": {},
+   "source": [
+    "# [Even Fibonacci Numbers](https://projecteuler.net/problem=2)\n",
+    "\n",
+    "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",
+    "\n",
+    "Since this is a SageMath notebook, we'll use its functionality so we can keep our code simple like the problem."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "57b68465",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4613732"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(n for n in fibonacci_xrange(1, 4000000) if n % 2 == 0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eef788da",
+   "metadata": {},
+   "source": [
+    "Even without SageMath, it's easy to implement our own generator of the sequence up to $n$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "24a7c257",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def fib(n):\n",
+    "    a = 0\n",
+    "    b = 1\n",
+    "    while a <= n:\n",
+    "        yield a\n",
+    "        a, b = b, a + b"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b3293a7d",
+   "metadata": {},
+   "source": [
+    "## Relevant sequences\n",
+    "* Fibonacci numbers: [A000045](https://oeis.org/A000045)\n",
+    "* Partial sums of even Fibonacci numbers: [A099919](https://oeis.org/A099919)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}