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A165471
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Legendre symbol (n,65537).
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10
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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
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OFFSET
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0,1
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COMMENTS
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65537 is the 4th Fermat prime, A019434(4).
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LINKS
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PROG
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(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)))))))))
(Sage)
def A165471(n): return legendre_symbol(n, 65537)
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CROSSREFS
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KEYWORD
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sign,mult,easy
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AUTHOR
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STATUS
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approved
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