

A222299


Number of different Gaussian primes in the Gaussian prime spiral beginning at the nth positive real Gaussian prime (A002145).


3



8, 10, 172, 12, 168, 19, 19, 21, 21, 168, 14, 37, 37, 14, 18, 30, 68, 10, 10, 4, 10, 4, 29, 29, 32, 2484, 58, 30, 32, 2484, 76, 16, 10, 10, 18, 23, 23, 1861, 1861, 30, 34, 958, 126, 22, 10, 182, 10, 10, 74, 10, 112, 26, 48, 29, 29, 774, 13, 13, 26, 774, 18, 10
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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

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, 31 + 4i, 41 + 4i, 41  4i, 31  4i, 31}. But only 19 are unique.


MATHEMATICA

loop2[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[Union[lst]]]; cp = Select[Range[1000], PrimeQ[#, GaussianIntegers > True] &]; Table[loop2[p], {p, cp}]


CROSSREFS

Sequence in context: A070276 A002286 A256877 * A070478 A306527 A347306
Adjacent sequences: A222296 A222297 A222298 * A222300 A222301 A222302


KEYWORD

nonn


AUTHOR

T. D. Noe, Feb 25 2013


STATUS

approved



