Project Euler Problem 65

peuler-65.ipynb

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   "cell_type": "code",
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   "source": [
    "import sympy\n",
    "import numpy as np"
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([2, 1])\n",
    "for k in range(1,100):\n",
    "    arr = np.append(arr, [2*k, 1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{6963524437876961749120273824619538346438023188214475670667}{2561737478789858711161539537921323010415623148113041714756}$"
      ],
      "text/plain": [
       "6963524437876961749120273824619538346438023188214475670667/2561737478789858711161539537921323010415623148113041714756"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one = sympy.symbols('1')\n",
    "p = sympy.symbols('p')\n",
    "\n",
    "def pack(e, z):\n",
    "    return e.subs(p, z + 1 / p)\n",
    "t = p\n",
    "\n",
    "for k in arr[0:99]:\n",
    "    t = pack(t, k)\n",
    "t.replace(p, 1).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6963524437876961749120273824619538346438023188214475670667/2561737478789858711161539537921323010415623148113041714756\n"
     ]
    }
   ],
   "source": [
    "print(t.replace(p, 1).simplify())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "272"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = 0\n",
    "for k in '6963524437876961749120273824619538346438023188214475670667':\n",
    "    s+=int(k)\n",
    "s"
   ]
  }
 ],
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