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   "source": [
    "# [Lychrel Numbers](https://projecteuler.net/problem=55)\n",
    "\n",
    "This could get tricky if we were working with fixed size integers, since the reverse-and-add process for [Lychrel numbers](https://en.wikipedia.org/wiki/Lychrel_number) can result in some big numbers. But Python ints have unlimited precision, so no need to worry about that."
   ]
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   "source": [
    "def is_palindrome(n):\n",
    "    s = str(n)\n",
    "    return s == s[::-1]\n",
    "\n",
    "\n",
    "def is_lychrel_number(n):\n",
    "    for _ in range(0, 50):\n",
    "        rev = int(str(n)[::-1])\n",
    "        n += rev\n",
    "        if is_palindrome(n):\n",
    "            return False\n",
    "        \n",
    "    return True"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d45f3460",
   "metadata": {},
   "source": [
    "This is easy to brute force, since we're not checking that many numbers, and we loop at most 50 times in our test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e473996a",
   "metadata": {},
   "outputs": [],
   "source": [
    "lychrel_numbers = {n for n in range(1, 10000) if is_lychrel_number(n)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2c3f1cbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "249"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(lychrel_numbers)"
   ]
  },
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   "cell_type": "markdown",
   "id": "ef8a3b03",
   "metadata": {},
   "source": [
    "## Relevant sequences\n",
    "* Suspected Lychrel numbers: [A023108](https://oeis.org/A023108)\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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