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A165601
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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.
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13
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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; internal format)
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OFFSET
| 0,3
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LINKS
| A. Karttunen, Table of n, a(n) for n = 0..269535
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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)))))))))
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CROSSREFS
| Trisections: A165604, A165605, A165606. Cf. A165602-A165603, A165460, A166045-A166047.
Sequence in context: A092962 A112924 A153092 * A054263 A178775 A124874
Adjacent sequences: A165598 A165599 A165600 * A165602 A165603 A165604
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 06 2009
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