A165472 -id:A165472 - cp's OEIS frontend

A165471 Legendre symbol (n,65537).

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 21 2009

65537 is the 4th Fermat prime, A019434(4).

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

Partial sums: A165472.

a(n)=kronecker(n,65537) \\ Charles R Greathouse IV, Oct 31 2011

def A165471(n): return legendre_symbol(n,65537)
[A165471(n) for n in range(82)]  # Peter Luschny, Aug 09 2012

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 *)

A268819 Column 32769 of array A269158: a(n) = F(n,65537), function F as defined in A269158.

Original entry on oeis.org

0, 98305, 3, 0, 6, 98306, 2, 98305, 12, 98311, 14, 3, 1, 98307, 9, 0, 24, 98317, 24, 6, 16, 98319, 27, 98306, 0, 98304, 23, 2, 30, 98312, 2, 98305, 48, 98329, 0, 12, 52, 98329, 6, 98311, 3, 98321, 3, 14, 14, 98330, 3, 3, 41, 98305, 43, 1, 4, 98326, 45, 98307, 6, 98335, 43, 9, 27, 98307, 19, 0, 27, 98353, 2, 24, 100, 98305, 1

Offset: 1

Antti Karttunen, Feb 25 2016

Terms a(1) .. a(65536) occur as column 32769 in arrays A268728 and A269158.

Antti Karttunen, Table of n, a(n) for n = 1..65536

Cf. A010873, A052928, A165471, A165472.
Cf. arrays A268728 and A269158.
Cf. A269157 (indices of zeros).

;; Two variants, both give same results in range n=1..65536:
(define (A268819 n) (A268728auxbi n 65537))
(define (A268819 n) (A269158auxbi n 65537))

a(n) = F(n,65537) = A269158(n,32769), function F as defined in A269158.
Other identities. For n = 1..65536:
a(n) = A268728(n,32769).
A165471(n) = 1 - A010873(A052928(a(n))).

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.

A179416 a(n)=1 if (n modulo 65536)+1 is a quadratic residue of 65537, 0 otherwise.

Original entry on oeis.org

1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0

Offset: 0

Antti Karttunen, Jul 27 2010

nonn

This sequence gives essentially the same information as A165471, but in contrast to it (and A165472), the period of this sequence is explicitly defined as 65536 (instead of 65537), so that in essence the zeros at A165471(k*65537) are silently skipped. Several derived sequences to be computed.

A. Karttunen, Table of n, a(n) for n = 0..65535

def A179416_list(n) :  # for n <= 65536
    Q = quadratic_residues(65537)
    return [int(i in Q) for i in (1..n)]
A179416_list(102) # Peter Luschny, Aug 08 2012

a(n) = 1 if A165471(1+(n%65536))=+1, otherwise 0. Period 65536.

cp's OEIS Frontend

A165471 Legendre symbol (n,65537).

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A165575 Partial sums of A165573.

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A165579 Partial sums of A011628.

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A268819 Column 32769 of array A269158: a(n) = F(n,65537), function F as defined in A269158.

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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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A179416 a(n)=1 if (n modulo 65536)+1 is a quadratic residue of 65537, 0 otherwise.

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