A193688 Number of steps to reach 1 in Collatz (3x+1) problem starting with 2^n - 1.

0, 7, 16, 17, 106, 107, 46, 47, 61, 62, 156, 157, 158, 159, 129, 130, 224, 225, 177, 178, 303, 304, 473, 474, 444, 445, 384, 385, 448, 449, 450, 451, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 852

Offset: 1

Author

Arkadiusz Wesolowski, Aug 02 2011

Keywords

• nonn

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Collatz Problem
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A000225, A006577, A179118 (starting with 2^n+1).

Programs

Mathematica

Table[Length[NestWhileList[If[OddQ@#, 3 # + 1, #/2] &, 2^n - 1, # > 1 &]] - 1, {n, 60}] (* Arkadiusz Wesolowski, Sep 16 2011 *)

Python

for i in range(1, 100):
    n = 2**i - 1
    x = n
    c = 0
    while x != 1:
        c = c + 1
        if (x & 1) == 0:
            x = x//2
        else:
            x = 3*x + 1
    print(c)
# David Rabahy, Sep 18 2017

Formula

For larger n, a(n) ~ 13.5*n.

a(n) = A006577(A000225(n)). - Michel Marcus, Jul 11 2023

a(2n) = 1 + a(2n-1) for n >= 2. - Alexandre Herrera, Jul 11 2023