A166049 Integers of the form 4n+1 for which Sum_{i=1..u} J(i,4n+1) is never negative for any u in range [1,(2n)], where J(i,k) is the Jacobi symbol.

1, 5, 9, 13, 21, 25, 37, 49, 81, 85, 93, 121, 165, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, 1521, 1681, 1849, 2025, 2209, 2401, 2601, 2809, 3025, 3249, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241

Offset

1,2

Links

Table of n, a(n) for n=1..47.

Prog

(Sage)
def is_Motzkin(n, k):
    s = 0
    for i in (1..k):
        s += jacobi_symbol(i, n)
        if s < 0: return False
    return True
def A166049_list(n):
    return [m for m in range(1, n + 1, 4) if is_Motzkin(m, m // 2)]
A166049_list(6241) # Peter Luschny, Aug 08 2012

Crossrefs

a(n) = A016813(A166048(n)). Union of A016754 and A166051.

Sequence in context: A057961 A314792 A089217 * A334214 A053411 A332571

Adjacent sequences: A166046 A166047 A166048 * A166050 A166051 A166052

Keyword

nonn

Author

Antti Karttunen, Oct 08 2009

Status

approved