A179416 - OEIS

A179416

a(n)=1 if (n modulo 65536)+1 is a quadratic residue of 65537, 0 otherwise.

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

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OFFSET

0,1

COMMENTS

This sequence gives essentially the same information as A165471, but in contrast to it (and A165472), the period of this sequence is explicitly defined as 65536 (instead of 65537), so that in essence the zeros at A165471(k*65537) are silently skipped. Several derived sequences to be computed.

LINKS

A. Karttunen, Table of n, a(n) for n = 0..65535

FORMULA

a(n) = 1 if A165471(1+(n%65536))=+1, otherwise 0. Period 65536.

PROG

(MIT Scheme:)

(define (A179416 n) (1+halved (A165471 (1+ (modulo n 65536)))))

(define (1+halved n) (floor->exact (/ (1+ n) 2)))

(Sage)

def A179416_list(n) : # for n <= 65536

Q = quadratic_residues(65537)

return [int(i in Q) for i in (1..n)]