A222596 Length of the closed curve through Gaussian primes described in A222594.

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

Offset: 1

Author

T. D. Noe, Feb 27 2013

Keywords

• nonn

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

Crossrefs

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

Programs

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