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%I A292254 #9 Sep 30 2017 16:06:29
%S A292254 0,1,2,2,4,4,4,4,8,8,8,9,8,8,8,8,16,16,16,16,16,16,18,19,16,16,16,17,
%T A292254 16,16,16,17,32,32,32,33,32,32,32,32,32,32,32,32,36,36,38,39,32,32,32,
%U A292254 32,32,32,34,34,32,32,32,32,32,32,34,35,64,64,64,64,64,64,66,67,64,64,64,65,64,64,64,65,64,64,64,65,64,64,64,64,72,72,72,72,76,76
%N A292254 a(n) = A292253(A163511(n)).
%C A292254 Because A292253(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 the numbers that are either of the form 12k+1 or of the form 12k+11 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 A292254 The AND - XOR formula just restates 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 A292254 Antti Karttunen, Table of n, a(n) for n = 0..8191
%H A292254 Index entries for sequences related to binary expansion of n
%H A292254 Index entries for sequences computed from indices in prime factorization
%F A292254 a(n) = A292253(A163511(n)).
%F A292254 a(n) = A292264(n) AND (A292274(n) XOR A292942(n)), where AND is bitwise-and (A004198) and XOR is bitwise-XOR (A003987). [See comments.]
%F A292254 For all n >= 0, a(n) + A292944(n) + A292256(n) = n.
%o A292254 (Scheme) (define (A292254 n) (A292253 (A163511 n)))
%Y A292254 Cf. A005940, A163511, A292253.
%Y A292254 Cf also A292247, A292248, A292256, A292264, A292271, A292274, A292592, A292593, A292942, A292944, A292946 (for similarly constructed sequences).
%K A292254 nonn
%O A292254 0,3
%A A292254 _Antti Karttunen_, Sep 28 2017
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