login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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. 10-16.

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), 79-99.

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), 3-23.

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 (* Jean-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified October 24 08:23 EDT 2014. Contains 248502 sequences.