A218217 a(n) = (x(n+1) - x(n))^2 + (y(n+1) - y(n))^2, where x(n)^2 + y(n)^2 = A055025(n) is norm of Gaussian prime and x(n) >= y(n) >= 0.

1, 2, 4, 2, 2, 2, 10, 20, 4, 10, 8, 4, 2, 10, 4, 20, 58, 16, 10, 2, 20, 58, 8, 40, 2, 40, 20, 10, 90, 2, 20, 10, 116, 2, 8, 20, 10, 68, 50, 10, 20, 26, 4, 146, 8, 34, 10, 40, 34, 40, 130, 104, 20, 2, 160, 50, 10, 180, 2, 180, 90, 58, 40, 130, 16, 116, 194, 50

Offset

1,2

Comments

We walk through the Gaussian primes in the first octant of the Gaussian plane along increasing norm: 1+i, 2+i, 3, 3+2i, 4+i, 5+2i, 6+i, 5+4i, 7, 7+2i etc. The sequence lists the squared distance between consecutive Gaussian primes along this walk.

Links

Table of n, a(n) for n=1..68.

Example

The squared distance between 5+4i and 6+i is (6-5)^2+(4-1)^2 =10 = a(7).

Mathematica

nMx = 1000; modLst = {2}; Do[p = Prime[n]; If[Mod[p, 4] == 1, AppendTo[modLst, p], If[p^2 < nMx, AppendTo[modLst, p^2]]], {n, 2, PrimePi[nMx]}]; modLst = Union[modLst]; last = {1, 1}; Table[pr = PowersRepresentations[n, 2, 2][[1]]; dist = SquaredEuclideanDistance[last, pr]; last = pr; dist, {n, Rest[modLst]}] (* T. D. Noe, Oct 29 2012 *)

Crossrefs

Cf. A055025.

Sequence in context: A179686 A286479 A013604 * A218279 A183193 A331470

Adjacent sequences: A218214 A218215 A218216 * A218218 A218219 A218220

Keyword

nonn

Author

Thomas Ordowski, Oct 23 2012

Status

approved