A165469 -id:A165469 - cp's OEIS frontend

A165468 a(n) = (A165469(n)-3)/4.

0, 1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 35, 37, 39, 41, 45, 47, 49, 53, 57, 59, 63, 65, 67, 71, 75, 77, 81, 83, 89, 95, 97, 99, 101, 107, 109, 111, 113, 117, 119, 125, 127, 129, 131, 133, 137, 139, 147, 149, 153, 155, 161, 165, 167, 169, 173, 179, 185, 187

Offset: 1

Antti Karttunen, Oct 06 2009

nonn

Subset of A095274. Cf. A165607.

A166092 Integers (all of the form 4k+3) organized into an array based on the number of times Sum_{i=1..u} J(i,4k+3) obtains value zero when u ranges from 1 to (4k+3), where J(i,k) is the Jacobi symbol.

Original entry on oeis.org

3, 7, 11, 15, 319, 19, 23, 607, 35, 415, 31, 703, 59, 1639, 91, 39, 895, 63, 2359, 175, 43, 47, 1063, 103, 3995, 575, 127, 51, 55, 1103, 131, 5191, 631, 295, 83, 67, 71, 1135, 251, 5459, 731, 635, 223, 115, 27, 79, 1447, 279, 7567, 1175, 659, 735, 139

Offset: 0

Antti Karttunen, Oct 08 2009

Note: these are all of the form 4k+3, but still this is not permutation of A004767 (for the reason explained in A166091). Sequence A165603 gives the 4k+3 integers missing from this table.This square array A(row>=0, col>=0) is listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

			The top left corner of the array:
3, 7, 15, 23, 31, 39, ...
11, 319, 607, 703, 895, 1063, ...
19, 35, 59, 63, 103, 131, ...
415, 1639, 2359, 3995, 5191, 5459, ...
91, 175, 575, 631, 731, 1175, ...

A. Karttunen, Table of n, a(n) for n = 0..10010

a(n) = A004767(A166091(n)). The leftmost column: A166096. The first five rows: A165469, A166053, A166055, A166057, A166059. Cf. also A112070.

A165608 Numbers of the form 4n+3 for which Sum_{i=1..u} J(i,4n+3) is never negative for any u in range [1,2n+1], but obtains at least one value zero, where J(i,m) is the Jacobi symbol.

Original entry on oeis.org

11, 27, 35, 59, 63, 75, 83, 103, 131, 135, 171, 175, 243, 251, 279, 295, 299, 319, 343, 351, 363, 371, 375, 395, 415, 419, 495, 539, 563, 567, 575, 607, 635, 659, 675, 703, 711, 731, 735, 755, 783, 867, 875, 895, 899, 903, 927, 943, 971, 999, 1063, 1067

Offset: 1

Antti Karttunen, Oct 06 2009

nonn

Setwise difference of A095100 and A165469.

a(n) = A004767(A165607(n)). Subset of A095100. A165977 gives the primes only. Cf. A165603.

Definition edited by Jonathan Sondow, Sep 27 2011

A165580 Primes of the form 4n+3 for which Sum_{i=1..u} J(i,4n+3) is never zero for any u in range [1,(2n+1)], where J(i,m) is the Jacobi symbol.

Original entry on oeis.org

3, 7, 23, 31, 47, 71, 79, 151, 167, 191, 199, 239, 263, 271, 311, 359, 383, 431, 439, 479, 503, 599, 647, 719, 743, 751, 839, 863, 887, 911, 919, 983, 991, 1031, 1039, 1151, 1223, 1231, 1279, 1319, 1399, 1439, 1471, 1487, 1511, 1559, 1583, 1759

Offset: 1

Antti Karttunen, Oct 06 2009

nonn

Setwise difference of A095102 and A165977. Also subset of A165469.

cp's OEIS Frontend

A165468 a(n) = (A165469(n)-3)/4.

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A166092 Integers (all of the form 4k+3) organized into an array based on the number of times Sum_{i=1..u} J(i,4k+3) obtains value zero when u ranges from 1 to (4k+3), where J(i,k) is the Jacobi symbol.

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A165608 Numbers of the form 4n+3 for which Sum_{i=1..u} J(i,4n+3) is never negative for any u in range [1,2n+1], but obtains at least one value zero, where J(i,m) is the Jacobi symbol.

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A165580 Primes of the form 4n+3 for which Sum_{i=1..u} J(i,4n+3) is never zero for any u in range [1,(2n+1)], where J(i,m) is the Jacobi symbol.

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