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%I M4335 #36 Nov 26 2022 12:43:33
%S 0,1,7,8,16,19,20,23,111,112,115,118,121,124,127,130,143,144,170,178,
%T 181,182,208,216,237,261,267,275,278,281,307,310,323,339,350,353,374,
%U 382,385,442,448,469,508,524,527,530,556,559,562,583,596,612,664,685,688,691,704
%N Record number of steps to reach 1 in '3x+1' problem, corresponding to starting values in A006877.
%C Both the 3x+1 steps and 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.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A006878/b006878.txt">Table of n, a(n) for n=1..130</a> (from Eric Roosendaal's data)
%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 J. C. Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html">The 3x+1 problem and its generalizations</a>, Amer. Math. Monthly, 92 (1985), 3-23.
%H G. T. Leavens and M. Vermeulen, <a href="/A006877/a006877_1.pdf">3x+1 search programs</a>, Computers and Mathematics with Applications, 24 (1992), 79-99. (Annotated scanned copy)
%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/delrecs.html">3x+1 Delay Records</a>
%H Robert G. Wilson v, <a href="/A006877/a006877.pdf">Letter to N. J. A. Sloane with attachments, Jan. 1989</a>
%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>
%p f := proc(n) local a,L; L := 0; a := n; while a <> 1 do if a mod 2 = 0 then a := a/2; else a := 3*a+1; fi; L := L+1; od: RETURN(L); end;
%t numberOfSteps[x0_] := Block[{x = x0, nos = 0}, While[x != 1, If[Mod[x, 2] == 0, x = x/2, x = 3*x+1]; nos++]; nos]; A006878 = numberOfSteps /@ A006877 (* _Jean-François Alcover_, Feb 22 2012 *)
%t DeleteDuplicates[Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]],{n,0,10^6}],GreaterEqual]-1 (* The program generates the first 44 terms of the sequence, derived from all starting values from 1 up to and including 1 million. *) (* _Harvey P. Dale_, Nov 26 2022 *)
%Y Cf. A006884, A006885, A006877, A033492, A033958, A033959.
%K nonn,nice
%O 1,3
%A _N. J. A. Sloane_, _Robert Munafo_
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