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%I #13 Oct 01 2017 00:29:09
%S 0,1,2,2,4,4,4,4,8,8,8,9,8,8,8,9,16,16,16,16,16,16,18,19,16,16,16,16,
%T 16,16,18,18,32,32,32,33,32,32,32,33,32,32,32,32,36,36,38,39,32,32,32,
%U 33,32,32,32,32,32,32,32,33,36,36,36,37,64,64,64,64,64,64,66,67,64,64,64,64,64,64,66,66,64,64,64,65,64,64,64,65,72,72,72,72,76,76
%N a(n) = A292941(A163511(n)).
%C Because A292941(n) = a(A243071(n)), the sequence works as a "masking function" where the 1-bits in a(n) (always a subset of the 1-bits in binary expansion of n) indicate which numbers are of the form 6k+1 in binary tree A163511 (or its mirror image tree A005940) on that trajectory which leads from the root of the tree to the node containing A163511(n).
%C The AND - XOR formula is just a restatement of the fact that J(-3|n) = J(-1|n)*J(3|n), as the Jacobi-symbol is multiplicative (also) with respect to its upper argument.
%H Antti Karttunen, <a href="/A292942/b292942.txt">Table of n, a(n) for n = 0..8191</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A292941(A163511(n)).
%F a(n) = A292264(n) AND (A292254(n) XOR A292274(n)), where AND is bitwise-and (A004198) and XOR is bitwise-XOR (A003987). [See comments.]
%F For all n >= 0, a(n) + A292944(n) + A292946(n) = n.
%o (Scheme) (define (A292942 n) (A292941 (A163511 n)))
%Y Cf. A005940, A163511, A292941.
%Y Cf. also A292247, A292248, A292254, A292256, A292264, A292271, A292274, A292592, A292593, A292944, A292946 (for similarly constructed sequences).
%K nonn
%O 0,3
%A _Antti Karttunen_, Sep 28 2017
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