A112082 -id:A112082 - cp's OEIS frontend

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

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.

A112055 a(n) = A112054(n)/6.

Original entry on oeis.org

2, 3, 5, 7, 8, 12, 13, 15, 17, 18, 20, 22, 23, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 47, 48, 50, 52, 53, 55, 57, 58, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 82, 83, 85, 87, 88, 90, 92, 93, 97, 98, 100, 102, 103, 107, 108, 110, 112, 113, 117, 118, 120, 122

Offset: 1

Antti Karttunen, Aug 27 2005

nonn

Cf. A112054, A112082 (complement), A112085 (first differences).

a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; Select[Range[1000], a112046[2#] - a112046[2# - 1] != 0 &]/6 (* Indranil Ghosh, May 25 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([n//6 for n in range(1, 201) if a(n)!=0]) # Indranil Ghosh, May 25 2017

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A112055 a(n) = A112054(n)/6.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python