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URL: https://oeis.org/A222594

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A222594
Length of the Gaussian prime spiral beginning at the n-th first-quadrant Gaussian prime (A222593).
3
4, 28, 28, 4, 12, 28, 28, 12, 4, 12, 4, 28, 12, 4, 12, 100, 4, 100, 12, 12, 28, 28, 12, 28, 28, 4, 260, 12, 12, 100, 12, 12, 100, 100, 4, 12, 4, 12, 260, 4, 4, 12, 260, 100, 12, 260, 260, 4, 4, 260, 260, 260, 100, 12, 100, 28, 260, 4, 12, 100, 12, 12, 260
OFFSET
1,1
COMMENTS
This is the idea of A222298 extended to first-quadrant Gaussian primes (A222593). It appears that all multiples of 4 eventually appear as a length.
REFERENCES
Joseph O'Rourke and Stan Wagon, Gaussian prime spirals, Mathematics Magazine, vol. 86, no. 1 (2013), p. 14.
EXAMPLE
The smallest such prime is 1 + i. The spiral is {1 + i, 2 + i, 2 - i, 1 - i, 1 + i}, which consists of only Gaussian primes.
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]]] - 1, {n, Length[ps]}]
CROSSREFS
Cf. A222298 (spiral lengths beginning at the n-th positive real Gaussian prime).
Sequence in context: A352838 A038706 A358863 * A153431 A043074 A137314
KEYWORD
nonn
AUTHOR
T. D. Noe, Feb 27 2013
STATUS
approved