A165477 -id:A165477 - cp's OEIS frontend

A165478 Positions of zeros in A165477.

0, 131070, 131071, 262141, 262142, 393212, 393213, 524283, 524284, 655354, 655355, 786425, 786426, 917496, 917497, 1048567, 1048568, 1179638, 1179639, 1310709, 1310710, 1441780, 1441781, 1572851, 1572852, 1703922, 1703923

Offset: 0

Antti Karttunen, Sep 21 2009

nonn

See also A165479. Compare also to A165473, A165483.

a(n) = floor(n/2)*131071 + (n modulo 2)*131070

A165479 a(n) = Least i in range [A165478(n),A165478(n+1)] for which abs(A165477(i)) gets the maximum value in that range.

Original entry on oeis.org

43690, 131070, 174761, 262141, 305832, 393212, 436903, 524283, 567974, 655354, 699045, 786425, 830116, 917496, 961187, 1048567, 1092258, 1179638, 1223329, 1310709, 1354400, 1441780, 1485471, 1572851, 1616542, 1703922

Offset: 0

Antti Karttunen, Sep 21 2009

nonn

The corresponding maximum values are 570,0,570,0,570,0,570,0,570,0,570,0,570,0,570,0,570,0,... (period 2 sequence). Note that also A165477(87380) = 570 (as 131071 is 4k+3 prime), and A165477(65535) = 285 = 570/2.

a(n) = floor(n/2)*131071 + (1+2*(n modulo 2))*43690

A165487 Squared version of A165477.

Original entry on oeis.org

0, 1, 4, 1, 4, 9, 4, 9, 16, 25, 36, 49, 36, 25, 36, 25, 36, 49, 64, 49, 64, 49, 64, 81, 64, 81, 64, 49, 64, 81, 64, 81, 100, 81, 100, 121, 144, 121, 100, 121, 144, 121, 100, 121, 144, 169, 196, 225, 196, 225, 256, 225, 196, 169, 144, 169, 196, 225, 256, 289, 256

Offset: 0

Antti Karttunen, Sep 21 2009

nonn

Period 131071. See comments in A165479.

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

a(n) = A000290(A165477(n)). Cf. A165486, A165488.

A165472 Partial sums of A165471.

Original entry on oeis.org

0, 1, 2, 1, 2, 1, 0, -1, 0, 1, 0, -1, -2, -1, -2, -1, 0, 1, 2, 3, 2, 3, 2, 1, 0, 1, 2, 1, 0, -1, 0, -1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 4, 3, 2, 1, 0, -1, -2, -1, 0, -1, 0, 1, 0, 1, 0, -1, -2, -3, -2, -3, -4, -5, -4, -5, -4, -5, -4, -3, -2, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, -2

Offset: 0

Antti Karttunen, Sep 21 2009

Period 65537.

Maximum value is 160 at a(65537n + 16382) and a(65537n + 16384); minimum value is -160 at a(65537n + 49152) and a(65537n + 49154). - Charles R Greathouse IV, Aug 06 2012

A. Karttunen, Table of n, a(n) for n = 0..65537

A165486 gives the squared version. Positions of zeros: A165473. See also A165474, A165475. Compare also to A165477, A165482.

A165482 Partial sums of A165481.

Original entry on oeis.org

0, 1, 2, 3, 4, 3, 4, 3, 4, 5, 4, 3, 4, 3, 2, 1, 2, 1, 2, 3, 2, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, -2, -1, 0, -1, 0, -1, -2, -1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -3, -4, -3, -2, -1, -2, -1, 0, -1, -2, -1, -2, -3, -2, -1, -2, -3, -4, -5, -4, -5, -4, -3, -4, -3, -2, -1, -2

Offset: 0

Antti Karttunen, Sep 21 2009

sign

Period 28657.

A. Karttunen, Table of n, a(n) for n = 0..28657

A165488 gives the squared version. Positions of zeros: A165483. See also A165484, A165485. Compare also to A165472, A165477.

A165582 Partial sums of A165581.

Original entry on oeis.org

0, 1, 2, 1, 2, 1, 0, -1, 0, 1, 0, -1, -2, -1, -2, -1, 0, -1, 0, -1, -2, -1, -2, -3, -4, -3, -2, -3, -4, -3, -2, -1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, -1, -2, -3, -4, -3, -2, -1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 3, 4, 3, 4, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 9, 8, 9, 8, 9, 10, 9, 10, 11, 10

Offset: 0

Antti Karttunen, Sep 22 2009

Period 524287. The largest value 658 occurs in four positions: a(184560) = a(184562) = a(339724) = a(339726) = 658. Note that a(262143) = 255 and a(174762) = a(349524) = 510. (Cf. to A165477 and see comments at A165479).

A. Karttunen, Table of n, a(n) for n = 0..524287

Positions of zeros: A165583. See also A165584, A165585. Similar sequences: A165472, A165477, A165482, A165575-A165579, A165582, A165587, A165592, A165597.

a(n)=sum(k=1,n%524287,kronecker(n,524287)) \\ Charles R Greathouse IV, Aug 06 2012

A165587 Partial sums of A165586.

Original entry on oeis.org

0, 1, 0, -1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 7, 6, 7, 6, 5, 6, 5, 6, 7, 6, 7, 6, 5, 4, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 7, 6, 5, 4, 5, 6, 5, 4, 3, 4, 5, 4, 5, 6, 5

Offset: 0

Antti Karttunen, Sep 22 2009

sign

Period 514229.

A. Karttunen, Table of n, a(n) for n = 0..514229

Positions of zeros: A165588. See also A165589, A165590. Similar sequences: A165472, A165477, A165482, A165575-A165579, A165582, A165587, A165592, A165597.

A165592 Partial sums of A165591.

Original entry on oeis.org

0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 4, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, -1, -2, -1, 0, -1, 0, -1, 0, -1, -2, -1, 0, 1, 2, 3, 2, 1, 2, 3, 2, 1, 0, -1, -2, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, -2, -1, -2, -1, 0, -1, -2, -3, -2, -1, -2, -3, -2, -3, -2, -1, -2, -3, -4

Offset: 0

Antti Karttunen, Sep 22 2009

sign

Period 59701.

A. Karttunen, Table of n, a(n) for n = 0..59701

Positions of zeros: A165593. See also A165594, A165595. Similar sequences: A165472, A165477, A165482, A165575-A165579, A165582, A165587, A165592, A165597.

A165597 Partial sums of A165596.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 8, 9, 10, 9, 10, 9, 10, 9, 8, 9, 10, 11, 12, 13, 12, 13, 14, 15, 16, 15, 14, 13, 14, 13, 12, 13, 14, 15, 14, 15, 14, 15, 16, 17, 18, 19, 20, 19, 20, 21, 22, 21, 20, 19, 20, 19, 20, 19, 20, 19, 20, 21, 20, 19, 18, 19, 18, 17, 18, 17, 16, 17

Offset: 0

Antti Karttunen, Sep 22 2009

sign

Period 59881.

First entry < 0: a(17698) = -1.

A. Karttunen, Table of n, a(n) for n = 0..59881

Positions of zeros: A165598. See also A165599, A165590. Similar sequences: A165472, A165477, A165482, A165575-A165579, A165582, A165587, A165592, A165597.

A165575 Partial sums of A165573.

Original entry on oeis.org

0, 1, 2, 1, 2, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 5, 6, 5, 4, 5, 6, 7, 8, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 5, 6, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 7, 8, 7, 6, 7, 8, 7, 8, 7, 8, 9, 8, 7, 6, 5, 4, 5, 4, 5, 4, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, -1, 0, 1, 2, 1

Offset: 0

Antti Karttunen, Sep 22 2009

sign

Period 257.

A. Karttunen, Table of n, a(n) for n = 0..59881

Similar sequences: A165576-A165579, A165472, A165477, A165482, A165582, A165587, A165592, A165597.

cp's OEIS Frontend

A165478 Positions of zeros in A165477.

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Formula

A165479 a(n) = Least i in range [A165478(n),A165478(n+1)] for which abs(A165477(i)) gets the maximum value in that range.

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Formula

A165487 Squared version of A165477.

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A165472 Partial sums of A165471.

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A165482 Partial sums of A165481.

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A165582 Partial sums of A165581.

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PARI

A165587 Partial sums of A165586.

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A165592 Partial sums of A165591.

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A165597 Partial sums of A165596.

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A165575 Partial sums of A165573.

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