A165461 -id:A165461 - cp's OEIS frontend

A165460 The height at the 1/3 point of Jacobi-bridge, computed for 12n+7. a(n) = Sum_{i=0..(4n+2)} J(i,12n+7), where J(i,m) is the Jacobi symbol.

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

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Conjecture: a(2n) = 2*A165605(2n) and a(2n+1) = (2/3)*A165605(2n+1). - Antti Karttunen, Oct 05 2009. (If true, then implies also the truth of conjecture in A165462.)

A. Karttunen, Table of n, a(n) for n = 0..21845

Cf. A165461, A165462, A165463, A165605.

Table[Sum[JacobiSymbol[i, 12n + 7], {i, 0, 4n + 2}], {n, 0, 100}] (* Indranil Ghosh, May 13 2017 *)

a(n) = sum(i=0, 4*n + 2, kronecker(i, 12*n + 7)); \\ Indranil Ghosh, May 13 2017

from sympy import jacobi_symbol as J
def a(n): return sum([J(i, 12*n + 7) for i in range(4*n + 3)]) # Indranil Ghosh, May 13 2017

A165605 Trisection 3n+1 of A165601.

Original entry on oeis.org

1, 3, 3, 3, 4, 3, 5, 6, 5, 6, 5, 9, 7, 3, 2, 6, 9, 9, 7, 6, 6, 12, 11, 9, 8, 9, 10, 9, 1, 12, 9, 9, 14, 6, 10, 6, 15, 18, 7, 0, 7, 9, 14, 15, 14, 9, 16, 15, 8, 12, 13, 15, 13, 9, 12, 12, 18, 15, 14, 12, 13, 15, 15, 12, 0, 15, 16, 21, 9, 18, 0, 21, 22, 9, 16, 9, 19, 0, 16, 12, 11, 24, 17

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Positions of zeros probably given by A165461. See the conjectures in A165460 and A165462.

A. Karttunen, Table of n, a(n) for n = 0..89844

a(n) = A165601(A016777(n)).

A165462 a(n) = (A165463(n)-3)/4.

Original entry on oeis.org

118, 193, 211, 232, 379, 493, 568, 574, 673, 868, 925, 943, 1243, 1261, 1300, 1318, 1372, 1408, 1471, 1618, 1693, 1702, 1816, 1993, 2068, 2290, 2323, 2368, 2389, 2395, 2437, 2443, 2512, 2731, 2743, 2797, 2818, 2968, 3106, 3118, 3193, 3235

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Conjecture: These are all those terms of A165602 which = 1 modulo 3. If this is true, then A165461 gives also the positions of zeros in A165605. - Antti Karttunen, Oct 05 2009

A. Karttunen, Table of n, a(n) for n = 0..1000

Cf. A165461-A165463. See also the conjecture in A165460.

cp's OEIS Frontend

A165460 The height at the 1/3 point of Jacobi-bridge, computed for 12n+7. a(n) = Sum_{i=0..(4n+2)} J(i,12n+7), where J(i,m) is the Jacobi symbol.

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A165605 Trisection 3n+1 of A165601.

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A165462 a(n) = (A165463(n)-3)/4.

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