A166050 - OEIS

%I #3 Mar 31 2012 13:21:20

%S 1,-1,3,-1,4,-1,5,-2,5,-2,5,-3,7,-1,2,-2,9,-3,7,-2,6,-4,11,-3,8,-3,10,

%T -3,1,-4,9,-3,14,-2,10,-2,15,-6,7,0,7,-3,14,-5,14,-3,16,-5,8,-4,13,-5,

%U 13,-3,12,-4,18,-5,14,-4,13,-5,15,-4,0,-5,16,-7,9,-6,0,-7,22,-3,16,-3

%N a(n) = Sum_{i=0..(2n+1)} J(i,12n+7), where J(i,k) is the Jacobi symbol.

%C The height at the 1/6 point of "Jacobi-bridge/path", computed for each odd integer of the form 12n+7.

%H A. Karttunen, <a href="/A166050/b166050.txt">Table of n, a(n) for n = 0..131071</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Jacobi_symbol">Jacobi symbol</a>

%o (MIT Scheme:) (define (A166050 n) (let ((w (A017605 n))) (add (lambda (i) (jacobi-symbol i w)) 0 (/ (-1+ w) 6))))

%Y Bisections: A166268, A166269 (see conjectures there). Cf. A017605. Scheme-code for jacobi-symbol is given at A165601.

%K sign

%O 0,3

%A _Antti Karttunen_, Oct 13 2009. Erroneous name corrected Oct 20 2009.