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Number of different Gaussian primes in the Gaussian prime spiral beginning at the n-th first-quadrant Gaussian prime (A222593).

4, 24, 24, 4, 8, 22, 22, 8, 4, 8, 4, 22, 8, 4, 10, 92, 4, 92, 10, 10, 22, 22, 10, 22, 22, 4, 172, 10, 10, 92, 10, 10, 92, 92, 4, 10, 4, 10, 172, 4, 4, 10, 172, 92, 10, 172, 172, 4, 4, 172, 172, 172, 92, 10, 92, 28, 172, 4, 12, 92, 10, 10, 172, 92, 4, 12, 172, 28

1,1

This is the idea of A222299 extended to first-quadrant Gaussian primes. The first odd number is a(79) = 29.

Joseph O'Rourke and Stan Wagon, Gaussian prime spirals, Mathematics Magazine, vol. 86, no. 1 (2013), p. 14.

T. D. Noe, <a href="/A222595/b222595.txt">Table of n, a(n) for n = 1..2829</a>

loop[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[lst]]; nn = 20; ps = {}; Do[If[PrimeQ[i + (j - i) I, GaussianIntegers -> True], AppendTo[ps, i + (j-i)*I]], {j, 0, nn}, {i, 0, j}]; Table[loop[ps[[n]]]; Length[Union[lst]], {n, Length[ps]}]

Cf. A222298 (spiral lengths beginning at the n-th positive real Gaussian prime).

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nonn

T. D. Noe, Feb 27 2013

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