Project Euler Q44 - LO Man Hei

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    "### Q44\n",
    "Find the pair of pentagonal numbers, \\(P_j\\) and \\(P_k\\), for which their sum and difference are pentagonal and \\( D = |P_k − P_j| \\) is minimised; what is the value of D?"
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    "def pentagonal_num(n):\n",
    "    return n*(3*n-1)//2\n",
    "\n",
    "def min_D():\n",
    "    pentagonal_num_dict = {}\n",
    "    found_pentagonal_num = set()\n",
    "    i = 1\n",
    "    while True:        \n",
    "        if i not in pentagonal_num_dict:\n",
    "            pentagonal_num_dict[i] = pentagonal_num(i)\n",
    "            found_pentagonal_num.add(pentagonal_num_dict[i])\n",
    "        for j in range(1,i)[::-1]:\n",
    "            if 2*pentagonal_num_dict[j] >= pentagonal_num_dict[i]:\n",
    "                continue\n",
    "            if (pentagonal_num_dict[i] - pentagonal_num_dict[j] in found_pentagonal_num and\n",
    "                pentagonal_num_dict[i] - 2*pentagonal_num_dict[j] in found_pentagonal_num):\n",
    "                return pentagonal_num_dict[i] - 2*pentagonal_num_dict[j]\n",
    "        i += 1"
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      "CPU times: user 250 ms, sys: 0 ns, total: 250 ms\n",
      "Wall time: 246 ms\n"
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   "source": [
    "%%time\n",
    "min_D()"
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