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A079260 Characteristic function of primes of form 4n+1 (1 if n is prime of form 4n+1, 0 otherwise). 10

%I

%S 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,

%T 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,

%U 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

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

%C 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).

%C a(A002144(n)) = 1; a(A137409(n)) = 0. [From _Reinhard Zumkeller_, Oct 11 2008]

%C a(n) * A151763(n) = a(n).

%H Reinhard Zumkeller, <a href="/A079260/b079260.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

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

%o (Haskell)

%o a079260 n = fromEnum $ n `mod` 4 == 1 && a010051 n == 1

%o -- _Reinhard Zumkeller_, Oct 06 2011

%Y Cf. A002144, A079261.

%Y Cf. A066339 (partial sums).

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 04 2003

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Last modified February 22 10:06 EST 2019. Contains 320390 sequences. (Running on oeis4.)