

A006878


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


13



0, 1, 7, 8, 16, 19, 20, 23, 111, 112, 115, 118, 121, 124, 127, 130, 143, 144, 170, 178, 181, 182, 208, 216, 237, 261, 267, 275, 278, 281, 307, 310, 323, 339, 350, 353, 374, 382, 385, 442, 448, 469, 508, 524, 527, 530, 556, 559, 562, 583, 596, 612, 664, 685, 688, 691, 704
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OFFSET

1,3


COMMENTS

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


REFERENCES

B. Hayes, Computer Recreations: On the ups and downs of hailstone numbers, Scientific American, 250 (No. 1, 1984), pp. 1016.
D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.
G. T. Leavens and M. Vermeulen, 3x+1 search problems, Computers and Mathematics with Applications, 24 (1992), 7999.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n=1..130 (from Eric Roosendaal's data)
J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 323.
Eric Roosendaal, 3x+1 Delay Records
Index entries for sequences from "Goedel, Escher, Bach"
Index entries for sequences related to 3x+1 (or Collatz) problem


MAPLE

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;


MATHEMATICA

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 (* JeanFrançois Alcover, Feb 22 2012 *)


CROSSREFS

Cf. A006884, A006885, A006877, A033492, A033958, A033959.
Sequence in context: A125195 A099534 A127933 * A022312 A055661 A054312
Adjacent sequences: A006875 A006876 A006877 * A006879 A006880 A006881


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane, Robert Munafo


STATUS

approved



