A232798 Sequence (or tree) generated by these rules: 1 is in S, and if x is in S, then x + 1, 3*x - 1 and 3*x + 1 are in S, and duplicates are deleted as they occur.

1, 2, 4, 3, 5, 7, 11, 13, 8, 10, 6, 14, 16, 20, 22, 12, 32, 34, 38, 40, 9, 23, 25, 29, 31, 17, 19, 15, 41, 43, 47, 49, 21, 59, 61, 65, 67, 35, 37, 33, 95, 97, 101, 103, 39, 113, 115, 119, 121, 26, 28, 24, 68, 70, 74, 76, 30, 86, 88, 92, 94, 18, 50, 52, 56

Offset

1,2

Comments

Let S be the sequence (or tree) of numbers defined by these rules: 1 is in S, and if x is in S, then x + 1, 3*x - 1, and 3*x + 1 are in S. Then S is a permutation of the positive integers. Deleting duplicates as they occur, the generations of S are given by g(1) = (1), g(2) = (2,4), g(3) = (3,5,7,11,13), etc. Concatenating these gives A232798. The position of n in S gives the inverse permutation of S, as in A232799.

Links

Clark Kimberling, Table of n, a(n) for n = 1..4000

Example

Each x begets x + 1, 3*x - 1 and 3*x + 1, but if any of these has already occurred it is deleted.  Thus, 1 begets (2,4); then 2 begets (3,5,7) and 4 begets (11,13), making g(3) = (3,5,7,11,13), etc.

Mathematica

x = {1}; Do[x = DeleteDuplicates[Flatten[Transpose[{x, x + 1, 3 x - 1, 3 x + 1}]]], {8}];  x (* A232798 *)
y = Flatten[Table[Position[x, n], {n, 1, 100}]] (* A232799 *)

Crossrefs

Cf. A232559, A232799.

Sequence in context: A343313 A082006 A277375 * A155850 A134464 A104472

Adjacent sequences: A232795 A232796 A232797 * A232799 A232800 A232801

Keyword

nonn,easy

Author

Clark Kimberling, Nov 30 2013

Status

approved