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

1,1

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.

Links

Table of n, a(n) for n=1..7.

Prog

(MIT Scheme with macro MATCHING-POS by AK):
(define (A166051 n) (A016813 (index_for_a166051 n)))
(define index_for_a166051 (MATCHING-POS 1 0 (lambda (n) (let ((w (A016813c n)) (hp (A005843 n))) (let loop ((i 1) (s 1)) (cond ((< s 0) #f) ((>= i hp) (zero? s)) (else (loop (1+ i) (+ s (jacobi-symbol (1+ i) w))))))))))
(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

Crossrefs

Setwise difference of A016754 and A166049.

Sequence in context: A273569 A273750 A191116 * A160170 A277189 A060004

Adjacent sequences: A166048 A166049 A166050 * A166052 A166053 A166054

Keyword

nonn

Author

Antti Karttunen, Oct 08 2009

Status

approved