Euler 045 - Triangular, Pentagonal, and Hexagonal.ipynb

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    "Euler Problem 45\n",
    "=================\n",
    "\n",
    "Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:\n",
    "\n",
    "Triangle\t \t$T_n=n(n+1)/2$\t \t1, 3, 6, 10, 15, ...\n",
    "\n",
    "Pentagonal\t \t$P_n=n(3n−1)/2$\t \t1, 5, 12, 22, 35, ...\n",
    "\n",
    "Hexagonal\t \t$H_n=n(2n−1)$\t \t1, 6, 15, 28, 45, ...\n",
    "\n",
    "It can be verified that T285 = P165 = H143 = 40755.\n",
    "\n",
    "Find the next triangle number that is also pentagonal and hexagonal."
   ]
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     "text": [
      "1\n",
      "40755\n",
      "1533776805\n",
      "57722156241751\n"
     ]
    }
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   "source": [
    "pentagon = 1\n",
    "hexagon = 1\n",
    "p_delta = 4\n",
    "h_delta = 5\n",
    "while hexagon < 10**15:\n",
    "    if pentagon == hexagon:\n",
    "        print(pentagon)\n",
    "    if pentagon <= hexagon:\n",
    "        pentagon += p_delta\n",
    "        p_delta += 3\n",
    "    elif pentagon > hexagon:\n",
    "        hexagon += h_delta\n",
    "        h_delta += 4"
   ]
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   "source": [
    "**Note:** All hexagonal numbers are also triangular, since $H_n = T_{2n-1}$."
   ]
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