OFFSET
1,2
COMMENTS
Let S be the sequence (or tree) of numbers generated by these rules: 1 and 2 are in S; if x is in S then x + 2 and 2*x are in S, where duplicates are deleted as they occur. Every positive integer occurs exactly once in S, so that S is a permutation of the natural numbers. Deleting duplicates as they occur, the generations of S are given by g(1) = (1,2), g(2) = (3,4), g(3) = (5,6,8), g(4) = (7,10,12,16), ... Concatenating gives 1,2,3,4,5,6,8,... Conjecture: the position of the n-th odd positive integer in S is the linearly recurrent sequence given by A232896(n) for n>=1.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
To generate S, start with g(1) = (1,2). Then 1 begets 3 and 2, but 2 is deleted as a duplicate, and 2 begets 4 and 4, of which the second 4 is deleted; thus g(2) = (3,4).
MATHEMATICA
x = {1, 2}; dx = 0; Do[x = DeleteDuplicates[Flatten[AppendTo[x, Transpose[{# + 2, 2*#}] &[Drop[x, Length[x] - dx]]]]]; dx = Length[x] - dx, {31}]; x (* A232895 *)
t = Flatten[Position[Denominator[x/2], 2]] (* A232896 conjectured *)
(* Peter J. C. Moses, Dec 02 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 02 2013
STATUS
approved