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A193688 Number of steps to reach 1 in Collatz (3x+1) problem starting with 2^n - 1. 4

%I #48 Aug 08 2023 18:39:38

%S 0,7,16,17,106,107,46,47,61,62,156,157,158,159,129,130,224,225,177,

%T 178,303,304,473,474,444,445,384,385,448,449,450,451,527,528,529,530,

%U 531,532,533,534,535,536,586,587,588,589,590,591,592,593,594,595,852

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

%H Arkadiusz Wesolowski, <a href="/A193688/b193688.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

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

%F a(n) = A006577(A000225(n)). - _Michel Marcus_, Jul 11 2023

%F a(2n) = 1 + a(2n-1) for n >= 2. - _Alexandre Herrera_, Jul 11 2023

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

%o (Python)

%o for i in range(1, 100):

%o n = 2**i - 1

%o x = n

%o c = 0

%o while x != 1:

%o c = c + 1

%o if (x & 1) == 0:

%o x = x//2

%o else:

%o x = 3*x + 1

%o print(c)

%o # _David Rabahy_, Sep 18 2017

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

%K nonn

%O 1,2

%A _Arkadiusz Wesolowski_, Aug 02 2011

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)