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A079261 Characteristic function of primes of form 4n+3 (1 if n is prime of form 4n+3, 0 otherwise). 10
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 (list; graph; refs; listen; history; text; internal format)
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 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

FORMULA

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

PROG

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

(Haskell)

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

-- Reinhard Zumkeller, Oct 06 2011

CROSSREFS

Cf. A002145, A079260.

Cf. A066490 (partial sums).

Sequence in context: A123740 A129272 A059648 * A073059 A156729 A049320

Adjacent sequences:  A079258 A079259 A079260 * A079262 A079263 A079264

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 04 2003

STATUS

approved

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Last modified December 16 09:34 EST 2018. Contains 318160 sequences. (Running on oeis4.)