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A166409
Odd numbers corresponding to the positions of zeros in A166406.
1
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 21 2009, Oct 22 2009
STATUS
approved