The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181777 Number of steps to reach 1 in '3x+1' (or Collatz) problem starting with the n-th Mersenne prime. 1
7, 16, 106, 46, 158, 224, 177, 450, 860, 1454, 1441, 1660, 6769, 8494, 17094, 29821, 30734, 43478, 55906, 60716, 129608, 134345, 153505, 265860, 293161, 312164, 598067, 1158876, 1482529, 1771117, 2906179, 10197081, 11568589, 16927967, 18807193, 40055567, 40663017, 93778449, 181209792, 282515044, 323346876, 349304386, 409093991, 438465334, 499902411, 573966881, 580260946 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Sequence currently gives the data for the 47 known Mersenne primes (A000043).
It is conjectured by Ohira and Watanabe that for large Mersenne primes 2^k-1, the fraction steps/k ~ 2+3*log(3)/log(4/3) or approximately 13.45.
The confirmed number of steps to reach 1 for other known Mersenne primes S(Mp) above 45th (M37156667): S(M42643801) = 573966881, S(M43112609) = 580260946, S(M57885161) = 779044992, S(M74207281) = 998401306. - Andrey S. Shchebetov and Sergei D. Shchebetov, Nov 14 2017
S(M77232917) = 1039248803. - Andrey S. Shchebetov and Sergei D. Shchebetov, Apr 25 2018
S(M82589933) = 1111148968. Also confirming all previous results. - Martin Raab, Apr 28 2023
LINKS
Andrey S. Shchebetov and Sergei D. Shchebetov, Table of n, a(n) for n = 1..47
T. Ohira and H. Watanabe, A Conjecture on the Collatz-Kakutani Path Length for the Mersenne Primes, arXiv:1104.2804 [math.NT], 2011-2012.
Martin Raab, PARI program
EXAMPLE
a(1)=7 as the first Mersenne prime is 3. So starting at 3 the steps are 10, 5, 16, 8, 4, 2, 1.
MATHEMATICA
collatz[k_] := (If[OddQ[k], j=3k+1, j=k/2]; j); step[m_] := (p=1; n=m; While[n!=1, (n=collatz[n]; p++)]; p-1); list = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951}; Table[step[2^s-1], {s, list}] (* warning: the list should be limited so as to run in a reasonable amount of time *)
PROG
(PARI) \\ See Raab link. \\ Martin Raab, May 11 2023
CROSSREFS
Sequence in context: A214904 A029498 A351531 * A332573 A129422 A184062
KEYWORD
nonn
AUTHOR
Frank M Jackson, Dec 23 2012
EXTENSIONS
a(43)-a(45) from Andrey S. Shchebetov and Sergei D. Shchebetov, Sep 22 2017
Edited by N. J. A. Sloane, Sep 26 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 03:10 EDT 2024. Contains 373492 sequences. (Running on oeis4.)