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A232895 Sequence (or tree) S of all positive integers in the order 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. 2
1, 2, 3, 4, 5, 6, 8, 7, 10, 12, 16, 9, 14, 20, 24, 18, 32, 11, 28, 22, 40, 26, 48, 36, 34, 64, 13, 30, 56, 44, 42, 80, 52, 50, 96, 38, 72, 68, 66, 128, 15, 60, 58, 112, 46, 88, 84, 82, 160, 54, 104, 100, 98, 192, 76, 74, 144, 70, 136, 132, 130, 256, 17, 62 (list; graph; refs; listen; history; text; internal format)
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

Cf. A232559, A232896.

Sequence in context: A114622 A125624 A262388 * A274607 A262374 A145518

Adjacent sequences:  A232892 A232893 A232894 * A232896 A232897 A232898

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 02 2013

STATUS

approved

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Last modified August 18 16:11 EDT 2017. Contains 290727 sequences.