A165575 -id:A165575 - cp's OEIS frontend

A165582 Partial sums of A165581.

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.

A165579 Partial sums of A011628.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 22 2009

sign

Period 233.

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

Similar sequences: A165575-A165578, A165472, A165477, A165482, A165582, A165587, A165592, A165597.

Table[ JacobiSymbol[n, 233], {n, 0, 96}] // Accumulate (* Jean-François Alcover, Oct 08 2013 *)

A165573 Legendre symbol (n,257).

Original entry on oeis.org

0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1

Offset: 0

Antti Karttunen, Sep 22 2009

257 is the 3rd Fermat prime, A019434(3).

A. Karttunen, Table of n, a(n) for n = 0..257

Partial sums: A165575.

a(n) = kronecker(n, 257); \\ Michel Marcus, Mar 12 2017

A165576 Partial sums of A165574.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 22 2009

nonn

Period 263. There are no negative values as 263 is one of the primes in A095102.

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

Similar sequences: A165575-A165579, A165472, A165477, A165482, A165582, A165587, A165592, A165597.

Accumulate[JacobiSymbol[Range[0,90],263]] (* Harvey P. Dale, Sep 01 2021 *)

A165578 Partial sums of A011627.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 22 2009

Period 229.

A. Karttunen, Table of n, a(n) for n = 0..229

Similar sequences: A165575-A165579, A165472, A165477, A165482, A165582, A165587, A165592, A165597.

Accumulate[JacobiSymbol[Range[0,120],229]] (* Harvey P. Dale, Feb 12 2022 *)

a(n)=sum(k=1,n%229,kronecker(k,229)) \\ Charles R Greathouse IV, Feb 11 2013

a(n) = -(a(n-1) + a(n-2) + ... + a(n-228)) = a(n-229). - Charles R Greathouse IV, Feb 11 2013

A165577 Partial sums of A011626.

Original entry on oeis.org

0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 3, 4, 3, 2, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 5, 6, 5, 6, 5, 4, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 2, 3, 2, 1, 0, 1, 0, 1, 0, -1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 10, 9

Offset: 0

Antti Karttunen, Sep 22 2009

sign

Period 227.

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

Similar sequences: A165575-A165579, A165472, A165477, A165482, A165582, A165587, A165592, A165597.

cp's OEIS Frontend

A165582 Partial sums of A165581.

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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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A165579 Partial sums of A011628.

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A165573 Legendre symbol (n,257).

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A165576 Partial sums of A165574.

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A165578 Partial sums of A011627.

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A165577 Partial sums of A011626.

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