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

Author

Alexis Monnerot-Dumaine, Jun 19 2019

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A126038, A005132, A128333.

Programs

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 *)