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.

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

Offset: 1

Author

Clark Kimberling, Dec 14 2013

Keywords

• nonn
• easy

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,...

Examples

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

Links

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

Crossrefs

Cf. A232559, A233560.

Programs

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 *)

Extensions

Name edited by Ivan Neretin, Nov 26 2016