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 A222300 Length of the closed curve through Gaussian primes described in A222298. 3

%I

%S 32,48,1316,72,1536,168,168,152,152,1536,140,352,352,132,172,280,648,

%T 132,92,12,96,32,332,332,460,30492,652,328,460,30492,748,236,64,112,

%U 204,336,336,24560,24560,448,440,13016,1536,316,108,2224,132,116,864,80,1128

%N Length of the closed curve through Gaussian primes described in A222298.

%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 A222298 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="/A222300/b222300.txt">Table of n, a(n) for n = 1..1000</a>

%e 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}. This loop is 168 units long.

%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]]; cp = Select[Range[1000], PrimeQ[#, GaussianIntegers -> True] &]; Table[loop[p]; Total[Abs[Differences[lst]]], {p, cp}]

%K nonn

%O 1,1

%A _T. D. Noe_, Feb 25 2013

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Last modified September 26 14:45 EDT 2021. Contains 347668 sequences. (Running on oeis4.)