eulerbooks/notebooks/problem0036.ipynb

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    "# [Double-base Palindromes](https://projecteuler.net/problem=36)\n",
    "\n",
    "Python's `bin` function converts an integer to a string representing the number in binary, starting with `0b`, so we'll just slice that off before we reverse and check if it's a [palindrome](https://en.wikipedia.org/wiki/Palindromic_number)."
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       "{1,\n",
       " 3,\n",
       " 5,\n",
       " 7,\n",
       " 9,\n",
       " 33,\n",
       " 99,\n",
       " 313,\n",
       " 585,\n",
       " 717,\n",
       " 7447,\n",
       " 9009,\n",
       " 15351,\n",
       " 32223,\n",
       " 39993,\n",
       " 53235,\n",
       " 53835,\n",
       " 73737,\n",
       " 585585}"
      ]
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   "source": [
    "is_base_2_palindrome = lambda x: bin(x)[2:] == bin(x)[:1:-1]\n",
    "is_base_10_palindrome = lambda x: str(x) == str(x)[::-1]\n",
    "\n",
    "double_palindromes = {n for n in range(1, 1000000) if is_base_2_palindrome(n) and is_base_10_palindrome(n)}\n",
    "double_palindromes"
   ]
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       "872187"
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   "source": [
    "sum(double_palindromes)"
   ]
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   "source": [
    "## Relevant sequences\n",
    "* Numbers that are base-2 and base-10 palindromes: [A007632](https://oeis.org/A007632)\n",
    "\n",
    "#### Copyright (C) 2025 filifa\n",
    "\n",
    "This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
   ]
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