login
This site is supported by donations 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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence currently limited to 42 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.

LINKS

Table of n, a(n) for n=1..42.

T. Ohira and H. Watanabe, A Conjecture on the Collatz-Kakutani Path Length for the Mersenne Primes

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++)]; 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 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

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified March 29 13:17 EDT 2017. Contains 284270 sequences.