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, 1-a}]]&, {0}, 9] (* Robert G. Wilson v, Jun 17 2014 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Clark Kimberling, Nov 28 2013
STATUS
approved