A112050 Length of the longest prefix of 1's in the Jacobi-vector {J(2n+1,1),J(2n+1,2),...,J(2n+1,2n)}.

1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 6, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 6, 4, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 6, 10, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 4, 12, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 6, 4, 1, 1, 2, 2, 1, 1

Offset: 1

Author

Antti Karttunen, Aug 27 2005

Keywords

• nonn

Crossrefs

Cf. A112046.

Programs

Mathematica

a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; Table[a112046[n] - 1, {n, 102}] (* Indranil Ghosh, May 24 2017 *)

Python

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(n) - 1
print([a(n) for n in range(1, 103)]) # Indranil Ghosh, May 24 2017

Formula

a(n) = A112046(n) - 1.

Extensions

Name clarified by Joerg Arndt, May 24 2017