A070976 Number of steps to reach 1 in '3x+1' (or Collatz) problem starting with 3^n.

0, 7, 19, 111, 22, 96, 33, 76, 75, 43, 135, 134, 133, 132, 144, 205, 129, 190, 140, 95, 94, 261, 428, 91, 258, 394, 331, 255, 254, 390, 389, 388, 462, 461, 460, 459, 458, 457, 456, 455, 454, 453, 501, 500, 450, 498, 497, 752, 495, 494, 493, 748, 491, 746, 489

Offset: 0

Author

Benoit Cloitre, May 17 2002

Keywords

• easy
• nonn

Comments

For all n, it appears that a(n) <= 37n. For n > 22, it appears that a(n) < 16n. - T. D. Noe, Feb 02 2007

This sequence contains some unusually long runs of values that differ by 1. - Dmitry Kamenetsky, Dec 09 2016

Examples

			For n=4, 3^4 = 81, and the Collatz sequence (3x + 1 if odd, x/2 if even) goes 81, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1.  This is 22 steps, so a(4) = 22. - _Michael B. Porter_, Dec 15 2016
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A279269, A277109. Equals A006577(3^n).

Programs

Mathematica

Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,3^n,#>1&]]-1, {n,0,60}] (* Harvey P. Dale, Oct 13 2011 *)

PARI

for(n=2,100,s=3^n; t=0; while(s!=1,t++; if(s%2==0,s=s/2,s=3*s+1); if(s==1,print1(t,","); ); ))

Formula

a(n) = A075487(n+1) = A074472(n) + 1. - T. D. Noe, Feb 02 2007