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Characteristic function of primes of form 4n+3 (1 if n is prime of form 4n+3, 0 otherwise).
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%I #23 Feb 06 2014 03:55:20

%S 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,

%T 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,

%U 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

%N Characteristic function of primes of form 4n+3 (1 if n is prime of form 4n+3, 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 is prime ==3 (mod 4).

%C a(A002145(n)) = 1; a(A145395(n)) = 0. [From _Reinhard Zumkeller_, Oct 12 2008]

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

%H Reinhard Zumkeller, <a href="/A079261/b079261.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = - A010051(n) * A011764(n+1). [_Reinhard Zumkeller_, Oct 06 2011]

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

%o (Haskell)

%o a079261 n = fromEnum $ n `mod` 4 == 3 && a010051 n == 1

%o -- _Reinhard Zumkeller_, Oct 06 2011

%Y Cf. A002145, A079260.

%Y Cf. A066490 (partial sums).

%K nonn

%O 1,1

%A _Benoit Cloitre_, Feb 04 2003