



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, 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, 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
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OFFSET

0,7


COMMENTS

In binary expansion (A007088) of n, clear the most significant bit and all those 1bits that have another 1bit at their left side, except for the second most significant 1bit, even in cases where the binary expansion begins as "11...".
Because A292943(n) = a(A243071(n)), the sequence works as a "masking function" where the 1bits in a(n) (always a subset of the 1bits 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).


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n


FORMULA

a(n) = A292272(A004754(n))  2*A053644(n).
a(n) = A292943(A163511(n)).
Other identities. For all n >= 0:
a(n) + A292264(n) = A292942(n) + a(n) + A292946(n) = a(n) + A292254(n) + A292256(n) = n.
a(n) = a(n) AND n; a(n) AND A292264(n) = 0, where AND is bitwiseand (A004198).


EXAMPLE

For n = 23, 10111 in binary, when we clear (change to zero) the most significant bit (always 1) and also all 1bits that have 1's at their left side, we are left with 100, which in binary stands for 4, thus a(23) = 4.
For n = 27, 11011 in binary, when we clear the most significant bit, and also all 1bits 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.


PROG

(Scheme)
(define (A292944 n) (let ((x (+ n (A053644 n)))) ( (A292272 x) (A053644 x))))
(define (A292944 n) ( (A292272 (A004754 n)) (* 2 (A053644 n))))
(define (A292944 n) (A292943 (A163511 n)))


CROSSREFS

Cf. A004754, A005940, A048735, A163511, A292272, A292943.
Cf. also A292247, A292248, A292254, A292256, A292264, A292271, A292274, A292592, A292593, A292942, A292946.
Sequence in context: A029368 A108483 A101565 * A327188 A330270 A029341
Adjacent sequences: A292941 A292942 A292943 * A292945 A292946 A292947


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Sep 28 2017


STATUS

approved



