euler57.ipynb

   1 {
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   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "$f(n) = 1 + \\frac{1}{1 + f(n-1)}$\n",
   8     "\n",
   9     "$f(1) = \\frac{3}{2}$\n",
  10     "\n",
  11     "$f(2) = 1 + \\frac{1}{1 + f(1)} = 1 + \\frac{1}{1 + \\frac{3}{2}} = 1 + \\frac{1}{\\frac{5}{2}} = 1 + \\frac{2}{5} = \\frac{7}{5}$\n",
  12     "\n",
  13     "$f(3) = 1 + \\frac{1}{1 + f(2)} = 1 + \\frac{1}{1 + \\frac{7}{5}} = 1 + \\frac{1}{\\frac{12}{5}} = 1 + \\frac{5}{12} = \\frac{17}{12}$\n",
  14     "\n",
  15     "$f(n) = 1 + \\frac{1}{1 + \\frac{n}{d}} = 1 + \\frac{1}{\\frac{n+d}{d}} = 1 + \\frac{d}{n+d} = \\frac{n+2d}{n+d}$"
  16    ]
  17   },
  18   {
  19    "cell_type": "code",
  20    "execution_count": 11,
  21    "metadata": {},
  22    "outputs": [
  23     {
  24      "data": {
  25       "text/plain": [
  26        "153"
  27       ]
  28      },
  29      "execution_count": 11,
  30      "metadata": {},
  31      "output_type": "execute_result"
  32     }
  33    ],
  34    "source": [
  35     "count = 0\n",
  36     "n, d = 3, 2\n",
  37     "(1..1000).each do\n",
  38     "  # puts \"#{n}, #{d}, #{n.to_s.length > d.to_s.length}\"\n",
  39     "  count += 1 if n.to_s.length > d.to_s.length\n",
  40     "  n, d = n + 2 * d, n + d\n",
  41     "end\n",
  42     "count"
  43    ]
  44   },
  45   {
  46    "cell_type": "code",
  47    "execution_count": null,
  48    "metadata": {
  49     "collapsed": true
  50    },
  51    "outputs": [],
  52    "source": []
  53   }
  54  ],
  55  "metadata": {
  56   "kernelspec": {
  57    "display_name": "Ruby 2.4.0",
  58    "language": "ruby",
  59    "name": "ruby"
  60   },
  61   "language_info": {
  62    "file_extension": ".rb",
  63    "mimetype": "application/x-ruby",
  64    "name": "ruby",
  65    "version": "2.4.0"
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  68  "nbformat": 4,
  69  "nbformat_minor": 2
  70 }