A222594 Length of the Gaussian prime spiral beginning at the n-th first-quadrant Gaussian prime (A222593).

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.

Links

T. D. Noe, Table of n, a(n) for n = 1..2829

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

Adjacent sequences: A222591 A222592 A222593 * A222595 A222596 A222597

Keyword

nonn

Author

T. D. Noe, Feb 27 2013

Status

approved