A165471 Legendre symbol (n,65537).

0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1

Offset

0,1

Comments

65537 is the 4th Fermat prime, A019434(4).

Links

A. Karttunen, Table of n, a(n) for n = 0..65537

Prog

(MIT Scheme, using fixnum-implementation of jacobi-symbol that works only up to 2^25-1 = 33554431):
(define (A165471 n) (legendre-symbol n 65537))
(define legendre-symbol jacobi-symbol)
(define jacobi-symbol fix:jacobi-symbol)
(define (fix:jacobi-symbol p q) (if (not (and (fix:fixnum? p) (fix:fixnum? q) (fix:= 1 (fix:and q 1)))) (error "fix:jacobi-symbol: args must be fixnums, and 2. arg should be odd: " p q) (let loop ((p p) (q q) (s 0)) (cond ((fix:zero? p) 0) ((fix:= 1 p) (fix:- 1 (fix:and s 2))) ((fix:= 1 (fix:and p 1)) (loop (fix:remainder q p) p (fix:xor s (fix:and p q)))) (else (loop (fix:lsh p -1) q (fix:xor s (fix:xor q (fix:lsh q -1)))))))))
(PARI) a(n)=kronecker(n, 65537) \\ Charles R Greathouse IV, Oct 31 2011
(Sage)
def A165471(n): return legendre_symbol(n, 65537)
[A165471(n) for n in range(82)]  # Peter Luschny, Aug 09 2012

Crossrefs

Partial sums: A165472.

Sequence in context: A011630 A011631 A165591 * A165481 A165573 A057428

Adjacent sequences: A165468 A165469 A165470 * A165472 A165473 A165474

Keyword

sign,mult,easy

Author

Antti Karttunen, Sep 21 2009

Status

approved