A166409 Odd numbers corresponding to the positions of zeros in A166406.

5, 13, 17, 21, 29, 33, 37, 41, 45, 53, 57, 61, 65, 69, 73, 77, 85, 89, 93, 97, 99, 101, 105, 109, 113, 117, 125, 129, 133, 137, 141, 145, 147, 149, 153, 157, 161, 165, 173, 177, 181, 185, 189, 193, 197, 201, 205, 207, 209, 213, 217, 221, 229, 233, 237, 241

Offset

1,1

Comments

Those odd numbers 2n+1 for which the sum of i in [1,2n+1] with J(i,2n+1)=-1 is equal to the sum of i in [1,2n+1] with J(i,2n+1)=+1. Here J(i,k) is the Jacobi symbol.

Probably a union of A077425 & A165603: It is clear that A077425 is a subsequence of this sequence. For the remaining terms to be equal to A165603, it is at least required that the intersection of A165603 and A095100 be empty.

Links

Table of n, a(n) for n=1..56.

Prog

(Python)
from sympy import jacobi_symbol as J
def a(n):
    l=0
    m=0
    for i in range(1, 2*n + 2):
        if J(i, 2*n + 1)==-1: l+=i
        elif J(i, 2*n + 1)==1: m+=i
    return l - m
print([2*n + 1 for n in range(201) if a(n)==0]) # Indranil Ghosh, Jun 12 2017

Crossrefs

Cf. A077425, A095100, A165603.

Sequence in context: A212287 A174361 A226165 * A077425 A039955 A213340

Adjacent sequences: A166406 A166407 A166408 * A166410 A166411 A166412

Keyword

nonn

Author

Antti Karttunen, Oct 21 2009, Oct 22 2009

Status

approved