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

1,1

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 A222298 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..1000

Example

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.

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}]

Crossrefs

Sequence in context: A043982 A236330 A045023 * A259770 A066472 A140172

Adjacent sequences: A222297 A222298 A222299 * A222301 A222302 A222303

Keyword

nonn

Author

T. D. Noe, Feb 25 2013

Status

approved