

A181777


Number of steps to reach 1 in '3x+1' (or Collatz) problem starting with the nth 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
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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^k1, 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


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 CollatzKakutani Path Length for the Mersenne Primes, arXiv:1104.2804 [math.NT], 20112012.
Wikipedia, Collatz conjecture


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++)]; p1); 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^s1], {s, list}] (* warning: the list should be limited so as to run in a reasonable amount of time *)


CROSSREFS

Cf. A000043, A006577, A070975, A193688.
Sequence in context: A192376 A214904 A029498 * A129422 A184062 A101122
Adjacent sequences: A181774 A181775 A181776 * A181778 A181779 A181780


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



