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filifa 2025-04-18 19:33:41 -04:00
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"$$g(n) = \\frac{2}{3}n^3 + \\frac{1}{2}n^2 + \\frac{4}{3}n - \\frac{3}{2}$$\n",
"Plugging in 1001, we get our answer: $g(1001) = 669171001$.\n",
"\n",
"Side note: this practice of writing the natural numbers in a spiral, combined with marking the prime numbers, has been coined the [Ulam spiral](https://en.wikipedia.org/wiki/Ulam_spiral). Somewhat interestingly, lots of primes appear in vertical, horiztonal, and diagonal lines when laid out this way.\n",
"Side note: this practice of writing the natural numbers in a spiral, combined with marking the prime numbers, has been coined the [Ulam spiral](https://en.wikipedia.org/wiki/Ulam_spiral). Somewhat interestingly, lots of primes appear in vertical, horizontal, and diagonal lines when laid out this way.\n",
"\n",
"## Relevant sequences\n",
"* Numbers on diagonals: [A200975](https://oeis.org/A200975)"