A166409 - OEIS

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

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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