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.

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

Offset: 1

Author

Antti Karttunen, Oct 08 2009

Keywords

• nonn

Comments

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.

Crossrefs

Setwise difference of A016754 and A166049.

Programs

Sage

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