A166268 -id:A166268 - cp's OEIS frontend

A166050 a(n) = Sum_{i=0..(2n+1)} J(i,12n+7), where J(i,k) is the Jacobi symbol.

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

Offset: 0

Antti Karttunen, Oct 13 2009. Erroneous name corrected Oct 20 2009

sign

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

A. Karttunen, Table of n, a(n) for n = 0..131071
Wikipedia, Jacobi symbol

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

A166270 Bisection 2n of A165460.

Original entry on oeis.org

2, 6, 8, 10, 10, 10, 14, 4, 18, 14, 12, 22, 16, 20, 2, 18, 28, 20, 30, 14, 14, 28, 28, 32, 16, 26, 26, 24, 36, 28, 26, 30, 0, 32, 18, 0, 44, 32, 38, 32, 22, 34, 32, 46, 38, 18, 44, 36, 32, 4, 36, 54, 24, 46, 22, 30, 48, 8, 54, 18, 46, 46, 40, 0, 38, 30, 44, 48, 44, 34, 36

Offset: 0

Antti Karttunen, Oct 13 2009

nonn

Conjecture: a(n) = 2*A166268(n).

A. Karttunen, Table of n, a(n) for n = 0..16383

a(n) = A165460(A005843(n)).

cp's OEIS Frontend

A166050 a(n) = Sum_{i=0..(2n+1)} J(i,12n+7), where J(i,k) is the Jacobi symbol.

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