{
 "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)\n",
    "\n",
    "#### Copyright (C) 2025 filifa\n",
    "\n",
    "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)."
   ]
  }
 ],
 "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
}