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%I #17 Sep 30 2017 16:07:29
%S 0,0,0,1,0,1,2,2,0,1,2,2,4,5,4,4,0,1,2,2,4,5,4,4,8,9,10,10,8,9,8,8,0,
%T 1,2,2,4,5,4,4,8,9,10,10,8,9,8,8,16,17,18,18,20,21,20,20,16,17,18,18,
%U 16,17,16,16,0,1,2,2,4,5,4,4,8,9,10,10,8,9,8,8,16,17,18,18,20,21,20,20,16,17,18,18,16,17,16,16,32,33,34,34,36,37,36,36
%N a(n) = A292272(A004754(n)) - 2*A053644(n).
%C In binary expansion (A007088) of n, clear the most significant bit and all those 1-bits that have another 1-bit at their left side, except for the second most significant 1-bit, even in cases where the binary expansion begins as "11...".
%C Because A292943(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+3 (odd multiples of three) 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).
%H Antti Karttunen, <a href="/A292944/b292944.txt">Table of n, a(n) for n = 0..16383</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = A292272(A004754(n)) - 2*A053644(n).
%F a(n) = A292943(A163511(n)).
%F Other identities. For all n >= 0:
%F a(n) + A292264(n) = A292942(n) + a(n) + A292946(n) = a(n) + A292254(n) + A292256(n) = n.
%F a(n) = a(n) AND n; a(n) AND A292264(n) = 0, where AND is bitwise-and (A004198).
%e For n = 23, 10111 in binary, when we clear (change to zero) the most significant bit (always 1) and also all 1-bits that have 1's at their left side, we are left with 100, which in binary stands for 4, thus a(23) = 4.
%e For n = 27, 11011 in binary, when we clear the most significant bit, and also all 1-bits that have 1's at their left side except the second most significant, we are left with 1010, which in binary stands for ten, thus a(27) = 10.
%o (Scheme)
%o (define (A292944 n) (let ((x (+ n (A053644 n)))) (- (A292272 x) (A053644 x))))
%o (define (A292944 n) (- (A292272 (A004754 n)) (* 2 (A053644 n))))
%o (define (A292944 n) (A292943 (A163511 n)))
%Y Cf. A004754, A005940, A048735, A163511, A292272, A292943.
%Y Cf. also A292247, A292248, A292254, A292256, A292264, A292271, A292274, A292592, A292593, A292942, A292946.
%K nonn,base
%O 0,7
%A _Antti Karttunen_, Sep 28 2017
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