A066861 For x > 0 let f(x) = x/2 if x is even, f(x) = (3*x+1)/2 if x is odd (3x+1 or Collatz problem). Sequence gives numbers such that k-1 applications of f lead to k for some k > 0.

1, 3, 4, 10, 11, 12, 18, 19, 24, 26, 32, 34, 35, 43, 49, 56, 58, 60, 61, 65, 66, 67, 80, 96, 104, 106, 113, 121, 130, 131, 132, 133, 134, 144, 145, 146, 147, 148, 149, 153, 156, 157, 158, 167, 169, 176, 180, 181, 184, 186, 192, 196, 197, 198, 200, 202, 204, 205, 206, 207, 222, 223, 246, 247, 249, 254, 255

Offset

1,2

Comments

Conjecture: a(n) = n*log(n) asymptotically.

Numbers n such that A258769(n)> 0. - Derek Orr, Jun 11 2015

Links

Table of n, a(n) for n=1..67.

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

f^(k-1)(n) = k.

Example

11 is in the sequence since seven applications of f lead to 8: 11 -> 17 -> 26 -> 13 -> 20 -> 10 -> 5 -> 8; 145 is in the sequence since 60 applications of f lead to 61.

Prog

(PARI) {for(n=1, 205, k=1; x=n; while(x!=1&&x!=k, x=if(x%2==0, x/2, (3*x+1)/2); k++); if(x==k, print1(n, ", ")))}

Crossrefs

Cf. A014682, A258769.

Sequence in context: A075100 A288660 A212440 * A292564 A191192 A139063

Adjacent sequences: A066858 A066859 A066860 * A066862 A066863 A066864

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 22 2002

Extensions

Edited by Klaus Brockhaus, May 26 2003

Status

approved