A165462 -id:A165462 - 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)).

A165602 Positions of zeros in A165601.

Original entry on oeis.org

24, 36, 51, 68, 78, 105, 118, 126, 132, 159, 186, 193, 211, 213, 222, 232, 240, 243, 267, 270, 294, 318, 321, 330, 348, 368, 375, 379, 402, 429, 443, 456, 465, 483, 493, 510, 537, 564, 568, 574, 575, 591, 618, 645, 672, 673, 693, 699, 708, 720, 722, 726

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

A. Karttunen, Table of n, a(n) for n = 0..21422

Cf. A165603, A165462.

A165463 Numbers of the form 12n+7 for which Sum_{i=0..(4n+2)} J(i,12n+7) = 0, where J(i,m) is the Jacobi symbol.

Original entry on oeis.org

475, 775, 847, 931, 1519, 1975, 2275, 2299, 2695, 3475, 3703, 3775, 4975, 5047, 5203, 5275, 5491, 5635, 5887, 6475, 6775, 6811, 7267, 7975, 8275, 9163, 9295, 9475, 9559, 9583, 9751, 9775, 10051, 10927, 10975, 11191, 11275, 11875, 12427

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Conjecture: a subset of A165603. See conjectures in A165460 and A165462.

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

a(n) = A004767(A165462(n)).

A165461 Positions of zeros in A165460.

Original entry on oeis.org

39, 64, 70, 77, 126, 164, 189, 191, 224, 289, 308, 314, 414, 420, 433, 439, 457, 469, 490, 539, 564, 567, 605, 664, 689, 763, 774, 789, 796, 798, 812, 814, 837, 910, 914, 932, 939, 989, 1035, 1039, 1064, 1078, 1106, 1112, 1155, 1164, 1189, 1253, 1280

Offset: 0

Antti Karttunen, Oct 06 2009

nonn

Also the positions of zeros in A165605 if the conjecture given in A165462 is true.

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

Cf. A165462-A165463.

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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A165602 Positions of zeros in A165601.

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A165463 Numbers of the form 12n+7 for which Sum_{i=0..(4n+2)} J(i,12n+7) = 0, where J(i,m) is the Jacobi symbol.

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A165461 Positions of zeros in A165460.

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