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 A222299 Number of different Gaussian primes in the Gaussian prime spiral beginning at the n-th positive real Gaussian prime (A002145). 3
 8, 10, 172, 12, 168, 19, 19, 21, 21, 168, 14, 37, 37, 14, 18, 30, 68, 10, 10, 4, 10, 4, 29, 29, 32, 2484, 58, 30, 32, 2484, 76, 16, 10, 10, 18, 23, 23, 1861, 1861, 30, 34, 958, 126, 22, 10, 182, 10, 10, 74, 10, 112, 26, 48, 29, 29, 774, 13, 13, 26, 774, 18, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Gaussian prime spiral is described in the short note by O'Rourke and Wagon. It is not known if every iteration is a closed loop. See A222298 for the number of line segments between primes. REFERENCES Joseph O'Rourke and Stan Wagon, Gaussian prime spirals, Mathematics Magazine, vol. 86, no. 1 (2013), p. 14. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE The loop beginning with 31 is {31, 43, 43 - 8i, 37 - 8i, 37 - 2i, 45 - 2i, 45 - 8i, 43 - 8i, 43, 47, 47 - 2i, 45 - 2i, 45 + 2i, 47 + 2i, 47, 43, 43 + 8i, 45 + 8i, 45 + 2i, 37 + 2i, 37 + 8i, 43 + 8i, 43, 31, 31 + 4i, 41 + 4i, 41 - 4i, 31 - 4i, 31}. But only 19 are unique. MATHEMATICA loop2[n_] := Module[{p = n, direction = 1}, lst = {n}; While[While[p = p + direction; ! PrimeQ[p, GaussianIntegers -> True]]; direction = direction*(-I); AppendTo[lst, p]; ! (p == n && direction == 1)]; Length[Union[lst]]]; cp = Select[Range[1000], PrimeQ[#, GaussianIntegers -> True] &]; Table[loop2[p], {p, cp}] CROSSREFS Sequence in context: A070276 A002286 A256877 * A070478 A306527 A347306 Adjacent sequences:  A222296 A222297 A222298 * A222300 A222301 A222302 KEYWORD nonn AUTHOR T. D. Noe, Feb 25 2013 STATUS approved

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Last modified September 24 14:46 EDT 2021. Contains 347643 sequences. (Running on oeis4.)