A165597 -id:A165597 - cp's OEIS frontend

A165598 Positions of zeros in A165597.

0, 17695, 17697, 17699, 17701, 17705, 17707, 17708, 17710, 17712, 17739, 17741, 17743, 17745, 17749, 17753, 17755, 17759, 17761, 17763, 17765, 17897, 17899, 17901, 17980, 17984, 17986, 18003, 18005, 18007, 18009, 18011, 18021, 18025

Offset: 0

Antti Karttunen, Sep 22 2009

nonn

A. Karttunen, Table of n, a(n) for n = 0..167

See also A165599, A165600. Compare also to A165593.

A165599 a(n) = Least i in range [A165598(n),A165598(n+1)] for which abs(A165597(i)) gets the maximum value in that range.

Original entry on oeis.org

5207, 17696, 17698, 17700, 17703, 17706, 17707, 17709, 17711, 17717, 17740, 17742, 17744, 17747, 17751, 17754, 17757, 17760, 17762, 17764, 17876, 17898, 17900, 17946, 17982, 17985, 17998, 18004, 18006, 18008, 18010, 18015, 18023

Offset: 0

Antti Karttunen, Sep 22 2009

nonn

A. Karttunen, Table of n, a(n) for n = 0..166

A165600 gives the corresponding maximum values.

A165600 A maximum absolute value of A165597 in range [A165598(n),A165598(n+1)].

Original entry on oeis.org

141, 1, -1, -1, -2, -1, 0, -1, -1, 5, -1, -1, 1, 2, -2, 1, -2, -1, -1, 1, -11, -1, 1, -10, -2, 1, -5, -1, -1, -1, 1, 4, 2, 18, -1, 42, 4, 1, -2, 81, 1, -1, 2, 0, 9, 3, 1, 2, 4, 5, -25, -1, -1, -16, -1, 4, 18, -1, 1, 2, 27, 1, 2, -1, 5, -1, -10, -1, -1, 1, -1, -1, -2, -1, 5, -1

Offset: 0

Antti Karttunen, Sep 22 2009

sign

Period 167. Cf. A165595.

A. Karttunen, Table of n, a(n) for n = 0..166

a(n) = A165597(A165599(n)).

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.

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.

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 *)

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

cp's OEIS Frontend

A165598 Positions of zeros in A165597.

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A165599 a(n) = Least i in range [A165598(n),A165598(n+1)] for which abs(A165597(i)) gets the maximum value in that range.

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A165600 A maximum absolute value of A165597 in range [A165598(n),A165598(n+1)].

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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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A165575 Partial sums of A165573.

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A165579 Partial sums of A011628.

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A165576 Partial sums of A165574.

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A165578 Partial sums of A011627.

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