A055026 Number of Gaussian primes of successive norms (indexed by A055025).

4, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8

Offset

1,1

Comments

These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).

References

R. K. Guy, Unsolved Problems in Number Theory, A16.

L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. V.

Links

Table of n, a(n) for n=1..87.

Index entries for Gaussian integers and primes

Example

There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).

Mathematica

m = 32; Length /@ Split[Sort[Select[Flatten[Table[{a^2 + b^2, a + b*I}, {a, -m, m}, {b, -m, m}], 1], PrimeQ[#[[2]], GaussianIntegers -> True] & ]], #1[[1]] == #2[[1]] & ][[1 ;; 87]] (* Jean-François Alcover, Apr 08 2011 *)

Crossrefs

Cf. A055025-A055029, A055664-...

Sequence in context: A010713 A105398 A005883 * A336818 A205681 A059163

Adjacent sequences: A055023 A055024 A055025 * A055027 A055028 A055029

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jun 09 2000

Extensions

More terms from Reiner Martin, Jul 20 2001

Status

approved