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A112050 Length of the longest prefix of 1's in the Jacobi-vector {J(2n+1,1),J(2n+1,2),...,J(2n+1,2n)}.

%I A112050 #19 May 09 2021 04:59:28
%S A112050 1,1,2,2,1,1,2,2,1,1,4,4,1,1,2,2,1,1,2,2,1,1,4,6,1,1,2,2,1,1,2,2,1,1,
%T A112050 6,4,1,1,2,2,1,1,2,2,1,1,4,4,1,1,2,2,1,1,2,2,1,1,6,10,1,1,2,2,1,1,2,2,
%U A112050 1,1,4,4,1,1,2,2,1,1,2,2,1,1,4,12,1,1,2,2,1,1,2,2,1,1,6,4,1,1,2,2,1,1
%N A112050 Length of the longest prefix of 1's in the Jacobi-vector {J(2n+1,1),J(2n+1,2),...,J(2n+1,2n)}.
%F A112050 a(n) = A112046(n) - 1.
%t A112050 a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; Table[a112046[n] - 1, {n, 102}] (* _Indranil Ghosh_, May 24 2017 *)
%o A112050 (Python)
%o A112050 from sympy import jacobi_symbol as J
%o A112050 def a112046(n):
%o A112050     i=1
%o A112050     while True:
%o A112050         if J(i, 2*n + 1)!=1: return i
%o A112050         else: i+=1
%o A112050 def a(n): return a112046(n) - 1
%o A112050 print([a(n) for n in range(1, 103)]) # _Indranil Ghosh_, May 24 2017
%Y A112050 Cf. A112046.
%K A112050 nonn
%O A112050 1,3
%A A112050 _Antti Karttunen_, Aug 27 2005
%E A112050 Name clarified by _Joerg Arndt_, May 24 2017