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

1,1

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

Mathematica

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

Prog

(PARI) { a(n)=if(n%4==1, isprime(n)) }; vector(100, n, a(n))
(Haskell)
a079260 n = fromEnum $ n `mod` 4 == 1 && a010051 n == 1
-- Reinhard Zumkeller, Oct 06 2011

Crossrefs

Cf. A002144, A079261.

Cf. A066339 (partial sums).

Sequence in context: A354948 A330551 A346618 * A358678 A359150 A354031

Adjacent sequences: A079257 A079258 A079259 * A079261 A079262 A079263

Keyword

nonn

Author

Benoit Cloitre, Feb 04 2003

Status

approved