A112059 -id:A112059 - cp's OEIS frontend

A112053 a(n) = A112046(2n) - A112046(2n-1) = A112048(n) - A112047(n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Antti Karttunen, Aug 27 2005

sign

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A112046, A112047, A112048.

Indices where a(n) is not zero: A112054. Values at those points: A112059.

a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; Table[a112046[2n] - a112046[2n - 1] , {n, 101}] (* Indranil Ghosh, May 24 2017 *)

from sympy import jacobi_symbol as J
def a112046(n):
    i=1
    while True:
        if J(i, 2*n + 1)!=1: return i
        else: i+=1
def a(n): return a112046(2*n) - a112046(2*n - 1)
print([a(n) for n in range(1, 102)]) # Indranil Ghosh, May 24 2017

a(n) = A112048(n)-A112047(n).

A112080 a(n) = difference between Jacobi-first-non-one(24n+1) and Jacobi-first-non-one(24n-1).

Original entry on oeis.org

0, 2, -2, 0, 4, 0, 8, -2, 0, 0, 0, 12, -6, 0, 12, 0, 2, -2, 0, -6, 0, 18, -6, 0, 0, 0, 2, -6, 0, -4, 0, 2, -2, 0, 18, 0, 2, -2, 0, 24, 0, 6, -2, 0, 0, 0, 6, -8, 0, 4, 0, 2, -2, 0, -6, 0, 32, -6, 0, 0, 0, 2, -6, 0, -10, 0, 2, -2, 0, 28, 0, 2, -2, 0, 4, 0, 38, -2, 0, 0, 0, 6, -6, 0, 4, 0, 2

Offset: 1

Antti Karttunen, Aug 27 2005

sign

The definition of Jacobi-first-non-one is given in A112056.

A. Karttunen, Table of n, a(n) for n = 1..4096

A112081(n) = a(n)/2. A112082 gives the points where a(n) is zero. A112059 gives the nonzero terms.

a(n) = 4*A112054(n)+1.

cp's OEIS Frontend

A112053 a(n) = A112046(2n) - A112046(2n-1) = A112048(n) - A112047(n).

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