A233560 -id:A233560

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A233559

Tree read by levels generated by these rules: 1 is at the top, and the node x has child nodes x+1, 2*x, and 3*x, where duplicates are deleted as they occur.

+10
2

1, 2, 3, 4, 6, 9, 5, 8, 12, 7, 18, 10, 27, 15, 16, 24, 13, 36, 14, 21, 19, 54, 11, 20, 30, 28, 81, 45, 17, 32, 48, 25, 72, 26, 39, 37, 108, 42, 22, 63, 38, 57, 55, 162, 33, 40, 60, 31, 90, 29, 56, 84, 82, 243, 46, 135, 34, 51, 64, 96, 49, 144, 50, 75, 73

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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), g(2) = (2,3), g(3) = (4,6,9), g(4) = (5,8,12,7,18,10,27), ... Concatenating gives 1,2,3,4,6,9,5,...

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..5000

EXAMPLE

To generate S, start with g(1) = (1). Then 1 begets 2 and 3; then 2 begets 4 and 3 begets 6 and 9.

MATHEMATICA

x = {1}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, x + 1, 2 x, 3 x}]]], {8}]; x (* A233559 *)

y = Flatten[Table[Position[x, n], {n, 1, 157}]] (* A233560 *)

CROSSREFS

Cf. A232559, A233560.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 14 2013

EXTENSIONS

Name edited by Ivan Neretin, Nov 26 2016

STATUS

approved

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