A033958 - OEIS

%I #36 Apr 01 2022 09:13:09

%S 1,3,7,9,25,27,73,97,129,171,231,313,327,703,871,1161,2463,2919,3711,

%T 6171,10971,13255,17647,23529,26623,34239,35655,52527,77031,106239,

%U 142587,156159,216367,230631,410011,511935,626331,837799,1117065,1501353,1723519,2298025,3064033

%N In the '3x+1' problem, these values for the starting value set new records for number of steps to reach 1.

%C Only the 3x+1 steps, not the halving steps, are counted.

%D D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.

%D G. T. Leavens and M. Vermeulen, 3x+1 search problems, Computers and Mathematics with Applications, 24 (1992), 79-99.

%H Charles R Greathouse IV, <a href="/A033958/b033958.txt">Table of n, a(n) for n = 1..71</a>

%H Brian Hayes, <a href="https://www.jstor.org/stable/24969271">Computer Recreations: On the ups and downs of hailstone numbers</a>, Scientific American, 250 (No. 1, 1984), pp. 10-16.

%H <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>

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

%F Positions of records in A006667. - _Sean A. Irvine_, Jul 22 2020

%t f[ nn_ ] := Module[ {c, n}, c = 0; n = nn; While[ n != 1, If[ Mod[ n, 2 ] == 0, n /= 2, n = 3*n + 1; c++ ] ]; Return[ c ] ] maxx = -1; For[ n = 1, n <= 10^8, n++, Module[ {val}, val = f[ n ]; If[ val > maxx, maxx = val; Print[ n, " ", val ] ] ] ] (* Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000 *)

%o (Haskell)

%o a033958 n = a033958_list !! (n-1)

%o -- For definition of a033958_list: see A033959.

%o -- _Reinhard Zumkeller_, Jan 08 2014

%Y Cf. A006884, A006885, A006877, A006878, A033492, A033959.

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Jud McCranie_, Jan 26 2000

%E Corrected with Mathematica code by Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000

%E a(40)-a(43) from _Charles R Greathouse IV_, Oct 07 2013