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 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 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 amount of time *) PROG (PARI) \\ See Raab link. \\ Martin Raab, May 11 2023 CROSSREFS Cf. A000043, A006577, A070975, A193688. Sequence in context: A214904 A029498 A351531 * A332573 A129422 A184062 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

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