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A165471 Legendre symbol (n,65537). 10
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 (list; graph; refs; listen; history; text; internal format)
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: A165591 * A165481 A165573 A057428 A165574 A165581

Adjacent sequences:  A165468 A165469 A165470 * A165472 A165473 A165474

KEYWORD

sign,mult,easy

AUTHOR

Antti Karttunen, Sep 21 2009

STATUS

approved

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Last modified February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)