The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 12:54 EST 2023. Contains 367727 sequences. (Running on oeis4.)