A079260 Characteristic function of primes of form 4n+1 (1 if n is prime of form 4n+1, 0 otherwise).

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

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 =2 or if n is prime ==1 (mod 4).

a(A002144(n)) = 1; a(A137409(n)) = 0. [From Reinhard Zumkeller, Oct 11 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. A002144, A079261.

Cf. A066339 (partial sums).

Programs

Haskell

a079260 n = fromEnum $ n `mod` 4 == 1 && a010051 n == 1
-- Reinhard Zumkeller, Oct 06 2011

Mathematica

Table[If[PrimeQ[n]&&IntegerQ[(n-1)/4],1,0],{n,120}] (* Harvey P. Dale, Jul 14 2015 *)

PARI

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