A308712 a(0) = 0 and a(1) = 1; for n > 1, a(n) = a(n-1)/2 if that number is an integer and not already in the sequence, otherwise a(n) = 3*a(n-1) + remainder of a(n-1)/2. (A variant of the Collatz sequence).

0, 1, 4, 2, 6, 3, 10, 5, 16, 8, 24, 12, 36, 18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 60, 30, 15, 46, 23, 70, 35, 106, 53, 160, 80, 240, 120, 360, 180, 90, 45, 136, 68, 204, 102, 51, 154, 77, 232, 116, 58, 29, 88, 44, 132, 66, 33, 100, 50, 25, 76, 38, 19, 58

Offset

0,3

Comments

Similar to A128333 and related to the 3x+1 (Collatz) sequence. Hits all positive integers?

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Example

a(1)=1 => a(2)=3*1+1=4 because a(1) is odd => a(3)=4/2=2 because a(2) is even => a(4)=3*2+0=6 because a(3) is even but a(3)/2 is already in the sequence.

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = With[{b = a[n-1]}, If[EvenQ[b] && FreeQ[Array[a, n, 0], b/2], b/2, 3 b + Mod[b, 2]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 20 2019 *)

Crossrefs

Cf. A126038, A005132, A128333.

Sequence in context: A349491 A097467 A169839 * A275845 A281978 A325887

Adjacent sequences: A308709 A308710 A308711 * A308713 A308714 A308715

Keyword

easy,nonn

Author

Alexis Monnerot-Dumaine, Jun 19 2019

Status

approved