A222595 Number of different Gaussian primes in the Gaussian prime spiral beginning at the n-th first-quadrant Gaussian prime (A222593).

4, 24, 24, 4, 8, 22, 22, 8, 4, 8, 4, 22, 8, 4, 10, 92, 4, 92, 10, 10, 22, 22, 10, 22, 22, 4, 172, 10, 10, 92, 10, 10, 92, 92, 4, 10, 4, 10, 172, 4, 4, 10, 172, 92, 10, 172, 172, 4, 4, 172, 172, 172, 92, 10, 92, 28, 172, 4, 12, 92, 10, 10, 172, 92, 4, 12, 172, 28

Offset

1,1

Comments

This is the idea of A222299 extended to first-quadrant Gaussian primes. The first odd number is a(79) = 29.

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..2829

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]]]; Length[Union[lst]], {n, Length[ps]}]

Crossrefs

Cf. A222298 (spiral lengths beginning at the n-th positive real Gaussian prime).

Sequence in context: A355992 A233149 A169688 * A103225 A303333 A324517

Adjacent sequences: A222592 A222593 A222594 * A222596 A222597 A222598

Keyword

nonn

Author

T. D. Noe, Feb 27 2013

Status

approved