A126038 -id:A126038 - cp's OEIS frontend

A128333 a(0) = 0; for n > 0, 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) + 1.

0, 1, 4, 2, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 25, 76, 38, 19, 58, 29, 88, 44, 133, 400, 200, 100, 50, 151, 454, 227, 682, 341, 1024, 512, 256, 128, 64, 32, 97, 292, 146, 73, 220, 110, 55, 166, 83, 250, 125, 376, 188, 94, 47, 142, 71, 214, 107, 322, 161

Offset: 0

Nick Hobson, Feb 27 2007

Other than a(0) = 0, the sequence misses all multiples of 3. Does it eventually hit all positive non-multiples of 3?

			Consider n = 3. We have a(3) = 2 and try to divide by 2. The result, 1, is certainly an integer, but we cannot use it because 1 is already in the sequence. So we must multiply by 3 and add 1 instead, getting a(4) = 3*2 + 1 = 7.

Nick Hobson, Table of n, a(n) for n = 0..10000
Nick Hobson, Python program
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A126038, A005132.

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).

Original entry on oeis.org

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

Alexis Monnerot-Dumaine, Jun 19 2019

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

			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.

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

Cf. A126038, A005132, A128333.

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 *)

cp's OEIS Frontend

A128333 a(0) = 0; for n > 0, 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) + 1.

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