A135461 a(n) = 1 if n is the norm of an Eisenstein prime (see A055664) otherwise 0.

0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset: 0

Author

N. J. A. Sloane, Feb 06 2008

Keywords

• nonn

Examples

			The smallest primes are 1-omega (of norm 3) and 2 (of norm 4).
		

References

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

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for characteristic functions

Crossrefs

Cf. A055667, A135462.

Characteristic function of A055664.

Programs

Mathematica

f[n_]:=If[ PrimeQ[n] && Mod[n, 6] == 1|| PrimeQ[Sqrt[n]] && Mod[Sqrt[n], 3] == 2||n==3,1,0];Array[f,99,0] (* James C. McMahon, Apr 15 2025 *)

PARI

A135461(n) = (isprime(n) && n%3<2) || (issquare(n, &n) && isprime(n) && n%3==2); \\ This is Charles R Greathouse IV's Apr 30 2013 code (with name "is") for A055664. - Antti Karttunen, Dec 06 2017