

A222596


Length of the closed curve through Gaussian primes described in A222594.


2



6, 64, 64, 8, 32, 92, 92, 32, 8, 32, 12, 92, 32, 12, 48, 412, 12, 412, 48, 48, 92, 92, 44, 92, 92, 12, 1316, 48, 44, 412, 48, 48, 412, 412, 24, 44, 24, 48, 1316, 12, 8, 48, 1316, 412, 44, 1316, 1316, 12, 12, 1316, 1316, 1316, 412, 44, 412, 204, 1316, 28, 72, 412
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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 A222594 and A222595 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..2829


MATHEMATICA

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 + (ji)*I]], {j, 0, nn}, {i, 0, j}]; Table[loop[ps[[n]]]; Total[Abs[Differences[lst]]], {n, Length[ps]}]


CROSSREFS

Cf. A222298 (spiral lengths beginning at the nth positive real Gaussian prime).
Sequence in context: A249590 A034665 A218383 * A067447 A083225 A320528
Adjacent sequences: A222593 A222594 A222595 * A222597 A222598 A222599


KEYWORD

nonn


AUTHOR

T. D. Noe, Feb 27 2013


STATUS

approved



