A079261 Characteristic function of primes of form 4n+3 (1 if n is prime of form 4n+3, 0 otherwise).

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

Offset: 1

Author

Benoit Cloitre, Feb 04 2003

Keywords

• nonn

Comments

Let M(n) denote the n X n matrix m(i,j)=0 if n divides ij-1, m(i,j) = 1 otherwise then det(M(n))=+1 if and only if n is prime ==3 (mod 4).

a(A002145(n)) = 1; a(A145395(n)) = 0. [From Reinhard Zumkeller, Oct 12 2008]

a(n) * A151763(n) = - a(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for characteristic functions

Crossrefs

Cf. A002145, A079260.

Cf. A066490 (partial sums).

Programs

Haskell

a079261 n = fromEnum $ n `mod` 4 == 3 && a010051 n == 1
-- Reinhard Zumkeller, Oct 06 2011

Mathematica

Table[If[PrimeQ[n]&&Mod[n,4]==3,1,0],{n,120}] (* Harvey P. Dale, Apr 26 2025 *)

PARI

{ a(n)=isprime(n)*if(n%4-3,0,1) }; vector(100,n,a(n))

Formula

a(n) = - A010051(n) * A011764(n+1). [Reinhard Zumkeller, Oct 06 2011]