cp's OEIS Frontend

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

%I A166409 #16 May 09 2021 08:05:05
%S A166409 5,13,17,21,29,33,37,41,45,53,57,61,65,69,73,77,85,89,93,97,99,101,
%T A166409 105,109,113,117,125,129,133,137,141,145,147,149,153,157,161,165,173,
%U A166409 177,181,185,189,193,197,201,205,207,209,213,217,221,229,233,237,241
%N A166409 Odd numbers corresponding to the positions of zeros in A166406.
%C A166409 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.
%C A166409 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.
%o A166409 (Python)
%o A166409 from sympy import jacobi_symbol as J
%o A166409 def a(n):
%o A166409     l=0
%o A166409     m=0
%o A166409     for i in range(1, 2*n + 2):
%o A166409         if J(i, 2*n + 1)==-1: l+=i
%o A166409         elif J(i, 2*n + 1)==1: m+=i
%o A166409     return l - m
%o A166409 print([2*n + 1 for n in range(201) if a(n)==0]) # _Indranil Ghosh_, Jun 12 2017
%Y A166409 Cf. A077425, A095100, A165603.
%K A166409 nonn
%O A166409 1,1
%A A166409 _Antti Karttunen_, Oct 21 2009, Oct 22 2009