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 A165601 Midpoint height of Jacobi-bridge, computed for 4n+3. a(n) = Sum_{i=0..(2n+1)} J(i,4n+3), where J(i,m) is the Jacobi symbol. 13
 1, 1, 3, 2, 3, 3, 1, 3, 6, 4, 3, 5, 6, 4, 9, 2, 3, 7, 2, 5, 9, 6, 6, 8, 0, 5, 9, 8, 6, 10, 6, 5, 15, 2, 9, 10, 0, 7, 12, 10, 3, 11, 6, 2, 15, 8, 6, 13, 12, 9, 12, 0, 9, 14, 12, 7, 15, 12, 6, 15, 1, 6, 21, 12, 12, 13, 6, 11, 0, 6, 9, 14, 12, 8, 24, 10, 9, 19, 0, 10, 12, 12, 9, 18, 18, 1, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS A. Karttunen, Table of n, a(n) for n = 0..269535 MATHEMATICA Table[Sum[JacobiSymbol[i, 4n + 3], {i, 0, 2n + 1}], {n, 0, 100}] (* Indranil Ghosh, May 13 2017 *) PROG (MIT Scheme:) (define (A165601 n) (let ((w (A004767 n))) (add (lambda (i) (jacobi-symbol i w)) 0 (/ (-1+ w) 2)))) (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i))))))) (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) = sum(i=0, 2*n + 1, kronecker(i, 4*n + 3)); \\ Indranil Ghosh, May 13 2017 (Python) from sympy import jacobi_symbol as J def a(n): return sum([J(i, 4*n + 3) for i in range(2*n + 2)]) # Indranil Ghosh, May 13 2017 CROSSREFS Trisections: A165604, A165605, A165606. Cf. A165602, A165603, A165460, A166045, A166046, A166047. Sequence in context: A230406 A214254 A153092 * A324030 A275821 A291674 Adjacent sequences:  A165598 A165599 A165600 * A165602 A165603 A165604 KEYWORD nonn AUTHOR Antti Karttunen, Oct 06 2009 STATUS approved

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Last modified May 16 13:21 EDT 2022. Contains 353704 sequences. (Running on oeis4.)