A039500 Iterations of "k->k/2 if k is even, k->3k-1 if k is odd" (A001281) starting at these numbers reach 1.

1, 2, 3, 4, 6, 8, 11, 12, 15, 16, 22, 24, 29, 30, 32, 39, 43, 44, 48, 53, 57, 58, 59, 60, 64, 65, 69, 71, 77, 78, 79, 85, 86, 87, 88, 95, 96, 97, 101, 103, 105, 106, 113, 114, 115, 116, 118, 120, 127, 128, 129, 130, 135, 137, 138, 141, 142, 145, 151, 154, 155, 156

Offset: 1

Author

Christian G. Bower, Feb 15 1999

Keywords

• nonn
• easy

Comments

It appears that lim_{n->oo} a(n)/n = 5/2. - Benoit Cloitre, Jan 29 2006

Equivalent to the Collatz ('3n+1') problem for negative integers. - Dmitry Kamenetsky, Jan 12 2017

There are 327679 terms in this sequence which are less than 1000000. Based on this, I would suggest that the limit of a(n)/n is more likely to be 3 than 5/2. This is also a natural guess; there are three known periodic orbits for this recurrence. - David Speyer, Mar 25 2022

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Positive integers not in A037084.

Cf. A039501, A039502, A039503, A039504, A039505.

Programs

Mathematica

colln[n_]:= NestWhile[If[EvenQ[#], #/2, 3#-1] &, n, FreeQ[{1, 5, 17}, #] &]; Select[Range[156], colln[#] == 1 &] (* Jayanta Basu, Jun 06 2013 *)