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A006877 In the `3x+1' problem, these values for the starting value set new records for number of steps to reach 1.
(Formerly M0748)
19

%I M0748

%S 1,2,3,6,7,9,18,25,27,54,73,97,129,171,231,313,327,649,703,871,1161,

%T 2223,2463,2919,3711,6171,10971,13255,17647,23529,26623,34239,35655,

%U 52527,77031,106239,142587,156159,216367,230631,410011,511935,626331,837799

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

%C Both the 3x+1 steps and the halving steps are counted.

%D Gonnet, Gaston H. "Computations on the 3n+ 1 conjecture." Maple Technical Newsletter 6 (1991): 18-22.

%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="/A006877/b006877.txt">Table of n, a(n) for n = 1..130</a> (from Eric Roosendaal's data)

%H T. Ahmed, H. Snevily, <a href="https://www.semanticscholar.org/paper/Are-There-an-Infinite-Number-of-Collatz-Integers-AHMED/2207919fcc0e2e4336faf345389c5dcd2daea50e">Are there an infinite number of Collatz integers?</a>, 2013.

%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 R. Munafo, <a href="http://www.mrob.com/pub/seq/wondrous.html">Integer Sequences Related to 3x+1 Collatz Iteration</a>

%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/delrecs.html">3x+1 Delay Records</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 A006877 := 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]; a[1] = 1; a[n_] := a[n] = Block[{x = a[n-1] + 1}, record = numberOfSteps[x - 1]; While[ numberOfSteps[x] <= record, x++]; x]; A006877 = Table[ Print[a[n]]; a[n], {n, 1, 44}](* _Jean-Fran├žois Alcover_, Feb 14 2012 *)

%o (PARI) A006577(n)=my(s);while(n>1,n=if(n%2,3*n+1,n/2);s++);s

%o step(n,r)=my(t);forstep(k=bitor(n,1),2*n,2,t=A006577(k);if(t>r,return([k,t])));[2*n,r+1]

%o r=0;print1(n=1);for(i=1,100,[n,r]=step(n,r); print1(", "n)) \\ _Charles R Greathouse IV_, Apr 01 2013

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

%K nonn,nice

%O 1,2

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

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Last modified September 23 13:55 EDT 2017. Contains 292358 sequences.