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A006878
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Record number of steps to reach 1 in `3x+1' problem, corresponding to starting values in A006877.
(Formerly M4335)
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13
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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
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1,3
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COMMENTS
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Both the 3x+1 steps and the halving steps are counted.
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REFERENCES
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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).
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LINKS
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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
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MAPLE
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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;
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MATHEMATICA
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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 (* From Jean-François Alcover, Feb 22 2012 *)
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CROSSREFS
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Cf. A006884, A006885, A006877, A033492, A033958, A033959.
Sequence in context: A125195 A099534 A127933 * A022312 A055661 A054312
Adjacent sequences: A006875 A006876 A006877 * A006879 A006880 A006881
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane, Robert Munafo
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STATUS
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approved
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