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A006878 Record number of steps to reach 1 in `3x+1' problem, corresponding to starting values in A006877.
(Formerly M4335)
14

%I M4335

%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 B. Hayes, Computer Recreations: On the ups and downs of hailstone numbers, Scientific American, 250 (No. 1, 1984), pp. 10-16.

%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 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 R. 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-Fran├žois Alcover_, Feb 22 2012 *)

%Y Cf. A006884, A006885, A006877, A033492, A033958, A033959.

%K nonn,nice,changed

%O 1,3

%A _N. J. A. Sloane_, _Robert Munafo_

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Last modified November 19 10:44 EST 2017. Contains 294936 sequences.