A213214 Number of steps to reach 1 in the Collatz (3x+1) problem starting with 3^n - 1.

1, 3, 10, 9, 96, 95, 32, 31, 43, 42, 134, 133, 132, 131, 99, 98, 190, 189, 139, 138, 261, 260, 427, 426, 394, 393, 330, 329, 390, 389, 388, 387, 461, 460, 459, 458, 457, 456, 455, 454, 453, 452, 500, 499, 498, 497, 496, 495, 494, 493, 492, 491, 746, 745, 488

Offset: 1

Author

Michel Lagneau, Mar 02 2013

Keywords

• nonn

Comments

It is interesting to note that the quantity 3^n - 1 appears in the Collatz trajectory of 2^n - 1 after n iterations (see the formula).

Examples

			a(8) = 31 because A193688(8)=47, and 47 - 2*8 = 31.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A212653, A075487, A193688.

Programs

Mathematica

f[n_]:=Module[{a=3^n-1, k=0}, While[a>1, k++; If[EvenQ[a], a=a/2, a=a*3+1]]; k]; Table[f[n], {n,100}]
Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,3^n-1,#>1&]]-1,{n,100}] (* Harvey P. Dale, Sep 06 2015 *)

Formula

a(n) = A193688(n) - 2*n for n > 1.