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A112053 a(n) = A112046(2n) - A112046(2n-1) = A112048(n) - A112047(n).

%I A112053 #13 Apr 28 2021 10:11:04
%S A112053 0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,
%T A112053 0,0,0,0,0,0,0,8,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A112053 0,0,0,12,0,0,0,0,0,-6,0,0,0,0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0
%N A112053 a(n) = A112046(2n) - A112046(2n-1) = A112048(n) - A112047(n).
%H A112053 Antti Karttunen, <a href="/A112053/b112053.txt">Table of n, a(n) for n = 1..10000</a>
%F A112053 a(n) = A112048(n)-A112047(n).
%t A112053 a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; Table[a112046[2n] - a112046[2n - 1] , {n, 101}] (* _Indranil Ghosh_, May 24 2017 *)
%o A112053 (Python)
%o A112053 from sympy import jacobi_symbol as J
%o A112053 def a112046(n):
%o A112053     i=1
%o A112053     while True:
%o A112053         if J(i, 2*n + 1)!=1: return i
%o A112053         else: i+=1
%o A112053 def a(n): return a112046(2*n) - a112046(2*n - 1)
%o A112053 print([a(n) for n in range(1, 102)]) # _Indranil Ghosh_, May 24 2017
%Y A112053 Cf. A112046, A112047, A112048.
%Y A112053 Indices where a(n) is not zero: A112054. Values at those points: A112059.
%K A112053 sign
%O A112053 1,12
%A A112053 _Antti Karttunen_, Aug 27 2005