

A222300


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


3



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
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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 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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



