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

32, 48, 1316, 72, 1536, 168, 168, 152, 152, 1536, 140, 352, 352, 132, 172, 280, 648, 132, 92, 12, 96, 32, 332, 332, 460, 30492, 652, 328, 460, 30492, 748, 236, 64, 112, 204, 336, 336, 24560, 24560, 448, 440, 13016, 1536, 316, 108, 2224, 132, 116, 864, 80, 1128

Offset: 1

Author

T. D. Noe, Feb 25 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 A222298 for the number of line segments between primes.

Examples

			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.
		

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..1000

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