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A232561 Sequence (or tree) generated by these rules: 1 is in S, and if x is in S, then x + 1 and 3*x are in S, and duplicates are deleted as they occur. 5
1, 2, 3, 6, 4, 9, 7, 18, 5, 12, 10, 27, 8, 21, 19, 54, 15, 13, 36, 11, 30, 28, 81, 24, 22, 63, 20, 57, 55, 162, 16, 45, 14, 39, 37, 108, 33, 31, 90, 29, 84, 82, 243, 25, 72, 23, 66, 64, 189, 60, 58, 171, 56, 165, 163, 486, 17, 48, 46, 135, 42, 40, 117, 38 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Let S be the set of numbers defined by these rules:  1 is in S, and if x is in S, then x + 1 and 3*x are in S.  Then S is the set of all positive integers, which arise in generations.  Deleting duplicates as they occur, the generations are given by g(1) = (1), g(2) = (2,3), g(3) = (6,4,9), g(4) = (7,18,5,8,10,27), etc.  Concatenating these gives A232561, a permutation of the positive integers.  The number of numbers in g(n) is A001590(n), the n-th tribonacci number.  It is helpful to show the results as a tree with the terms of S as nodes and edges from x to x + 1 if x + 1 has not already occurred, and an edge from x to 3*x if 3*x has not already occurred.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

Each x begets x + 1 and 3*x, but if either has already occurred it is deleted.  Thus, 1 begets 2 and 3; in the next generation, 2 begets only 6, and 3 begets 4 and 9.

MATHEMATICA

z = 8; g[1] = {1}; g[2] = {2, 3};

g[n_] := Riffle[g[n - 1] + 1, 3 g[n - 1]]

j[2] = Join[g[1], g[2]]; j[n_] := Join[j[n - 1], g[n]];

g1[n_] := DeleteDuplicates[DeleteCases[g[n], Alternatives @@ j[n - 1]]];

g1[1] = g[1]; g1[2] = g[2];

t = Flatten[Table[g1[n], {n, 1, z}]]  (* A232561 *)

Table[Length[g1[n]], {n, 1, z}]  (* A001590 *)

t1 = Flatten[Table[Position[t, n], {n, 1, 200}]]  (* A232562 *)

CROSSREFS

Cf. A232560, A232562, A001590.

Sequence in context: A103864 A268712 A152679 * A348395 A320123 A194357

Adjacent sequences:  A232558 A232559 A232560 * A232562 A232563 A232564

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 26 2013

STATUS

approved

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Last modified June 28 00:25 EDT 2022. Contains 354903 sequences. (Running on oeis4.)