{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hopfstader's functions are defined as below. Can we find a pattern? From a Tweet [insert link] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "H (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F(n) = n==0 ? 0 : n - F(n-1)\n",
    "G(n) = n==0 ? 0 : n - G(G(n-1))\n",
    "H(n) = n==0 ? 0 : n - H(H(H(n-1)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "ename": "BoundsError",
     "evalue": "BoundsError: attempt to access 121-element Array{Int64,1} at index [0]",
     "output_type": "error",
     "traceback": [
      "BoundsError: attempt to access 121-element Array{Int64,1} at index [0]",
      "",
      "Stacktrace:",
      " [1] getindex(::Array{Int64,1}, ::Int64) at ./array.jl:729",
      " [2] (::getfield(Main, Symbol(\"##11#12\")))(::Int64) at ./none:0",
      " [3] iterate at ./generator.jl:47 [inlined]",
      " [4] collect_to!(::Array{Int64,1}, ::Base.Generator{UnitRange{Int64},getfield(Main, Symbol(\"##11#12\"))}, ::Int64, ::Int64) at ./array.jl:651",
      " [5] collect_to_with_first!(::Array{Int64,1}, ::Int64, ::Base.Generator{UnitRange{Int64},getfield(Main, Symbol(\"##11#12\"))}, ::Int64) at ./array.jl:630",
      " [6] collect(::Base.Generator{UnitRange{Int64},getfield(Main, Symbol(\"##11#12\"))}) at ./array.jl:611",
      " [7] top-level scope at util.jl:156",
      " [8] top-level scope at In[11]:2"
     ]
    }
   ],
   "source": [
    "x = 0:120\n",
    "#f = [F(n) - F(n-1) for n in x]\n",
    "#g = [G(n) - G(n-1) for n in x]\n",
    "@time h = [n==0 ? 0 : n - h[h[h[n]]] for n in x]\n",
    "#plot(x,h,hs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in 1:50\n",
    "    for k in 1:200 - i\n",
    "        if h[i] != h[i+k]\n",
    "            print(\"Not \", i)\n",
    "            break\n",
    "        end\n",
    "    end\n",
    "end\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
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 "nbformat": 4,
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