

A232723


Sequence (or tree) generated by these rules: 0 is in S, and if x is in S, then 2*x and 1  x are in S, and duplicates are deleted as they occur.


5



0, 1, 2, 4, 1, 8, 3, 2, 16, 7, 6, 4, 3, 32, 15, 14, 12, 7, 8, 5, 6, 64, 31, 30, 28, 15, 24, 13, 14, 16, 9, 10, 12, 5, 128, 63, 62, 60, 31, 56, 29, 30, 48, 25, 26, 28, 13, 32, 17, 18, 20, 9, 24, 11, 10, 256, 127, 126, 124, 63
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OFFSET

1,3


COMMENTS

Let S be the set of numbers defined by these rules: 0 is in S, and if x is in S, then 2*x and 1  x are in S. Then S is the set of integers, which arise in generations. Deleting duplicates as they occur, the generations are given by g(1) = (0), g(2) = (1), g(3) = (2), g(4) = (4,1), g(5) = (8,3,2), etc. Concatenating these gives A232723. Every integer occurs exactly once in S. The even integers occupy the positions given by the lower Wythoff sequence, A000201; the odds, by the upper Wythoff sequence, A001950. The positive integers occupy the positions given by A189035, and the positions of the nonpositives, by A189034.
Inverse beginning with 0: 1, 2, 3, 13, 4, 20, 21, 18, 6, 31, 32, 89, 33, 28, 29, 26, 9, 49, 50, 136, 51, 143, 144, 141, 53, 44, ..., .  Robert G. Wilson v, Jun 17 2014


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


EXAMPLE

Each x begets 2*x and 1  x, and if either has already occurred it is deleted. Thus, 0 begets 1, which begets 2, which begets (4,1), etc.


MATHEMATICA

x = {0}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, 2*x, 1  x}]]], {10}]; x (* Peter J. C. Moses, Nov 28 2013 *)
Nest[ DeleteDuplicates[ Flatten[ # /. a_Integer > {2a, 1a}]]&, {0}, 9] (* Robert G. Wilson v, Jun 17 2014 *)


CROSSREFS

Cf. A232559, A226130, A226131, A000201, A189035.
Sequence in context: A087060 A248112 A173122 * A275486 A065278 A207605
Adjacent sequences: A232720 A232721 A232722 * A232724 A232725 A232726


KEYWORD

sign,easy


AUTHOR

Clark Kimberling, Nov 28 2013


STATUS

approved



