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 A185271 Differences between consecutive norms of Gaussian primes. 1
 3, 4, 4, 4, 12, 8, 4, 8, 4, 8, 12, 16, 8, 4, 8, 4, 8, 16, 12, 8, 16, 8, 12, 4, 32, 4, 8, 16, 12, 8, 4, 12, 20, 4, 20, 12, 4, 8, 12, 16, 8, 4, 8, 12, 12, 16, 8, 4, 48, 12, 8, 12, 16, 12, 8, 16, 8, 12, 4, 24, 12, 8, 12, 4, 24, 8, 24, 24, 4, 8, 4, 24, 12, 12, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If this sequence goes to infinity fast enough then the Gaussian moat-crossing problem is solved and it is impossible to walk to infinity in the complex plane using steps of bounded length stepping only on Gaussian primes. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Eric W. Weisstein, MathWorld: Gaussian Prime Eric W. Weisstein, MathWorld: Moat-Crossing Problem Wikipedia, Gaussian Integer FORMULA a(n) = A055025(n+1) - A055025(n). EXAMPLE The first Gaussian prime (restricting ourselves to the first octant) is 1+i which has norm 2 (1^2+1^2). The second is 2+i with norm 5 (2^2+1^2). The difference in those norms is 3, the first term in this sequence. CROSSREFS Cf. A055025 (norms of Gaussian primes). Sequence in context: A112180 A058559 A232092 * A158012 A032446 A271563 Adjacent sequences:  A185268 A185269 A185270 * A185272 A185273 A185274 KEYWORD nonn,easy AUTHOR Patrick P Sheehan, Jan 25 2012 STATUS approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)