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

1,2

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.

Sequence in context: A113197 A113199 A243572 * A285332 A344844 A185290

Adjacent sequences: A233556 A233557 A233558 * A233560 A233561 A233562

Keyword

nonn,easy

Author

Clark Kimberling, Dec 14 2013

Extensions

Name edited by Ivan Neretin, Nov 26 2016

Status

approved