A166049 -id:A166049 - cp's OEIS frontend

A166048 a(n) = (A166049(n)-1)/4.

0, 1, 2, 3, 5, 6, 9, 12, 20, 21, 23, 30, 41, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070

Offset: 1

Antti Karttunen, Oct 08 2009

nonn

Indexing sequence for A166049.

A166051 Nonsquare 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.

Original entry on oeis.org

5, 13, 21, 37, 85, 93, 165

Offset: 1

Antti Karttunen, Oct 08 2009

nonn

Conjecture: There are no more terms after 165. (Checked up to A016813(290511) = 1162045.) If this is true, then also 5, 13 and 37 are only 4k+1 primes in A080114.

Setwise difference of A016754 and A166049.

def is_what(n, k):
    s = 0
    for i in (1..k):
        s += jacobi_symbol(i, n)
        if s < 0: return False
    return not is_square(n)
def A166051_list(n):
    return [m for m in range(1, n + 1, 4) if is_what(m, m // 2)]
A166051_list(1000) # Peter Luschny, Aug 08 2012

cp's OEIS Frontend

A166048 a(n) = (A166049(n)-1)/4.

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A166051 Nonsquare 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.

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Sage