|
%I #3 Feb 27 2013 16:26:24
%S 6,64,64,8,32,92,92,32,8,32,12,92,32,12,48,412,12,412,48,48,92,92,44,
%T 92,92,12,1316,48,44,412,48,48,412,412,24,44,24,48,1316,12,8,48,1316,
%U 412,44,1316,1316,12,12,1316,1316,1316,412,44,412,204,1316,28,72,412
%N Length of the closed curve through Gaussian primes described in A222594.
%C 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 A222594 and A222595 for the number of line segments between primes.
%D Joseph O'Rourke and Stan Wagon, Gaussian prime spirals, Mathematics Magazine, vol. 86, no. 1 (2013), p. 14.
%H T. D. Noe, <a href="/A222596/b222596.txt">Table of n, a(n) for n = 1..2829</a>
%t 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]]]; Total[Abs[Differences[lst]]], {n, Length[ps]}]
%Y Cf. A222298 (spiral lengths beginning at the n-th positive real Gaussian prime).
%K nonn
%O 1,1
%A _T. D. Noe_, Feb 27 2013
|
