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A006885 Record highest point of trajectory before reaching 1 in '3x+1' problem, corresponding to starting values in A006884.
(Formerly M2086)
13
1, 2, 16, 52, 160, 9232, 13120, 39364, 41524, 250504, 1276936, 6810136, 8153620, 27114424, 50143264, 106358020, 121012864, 593279152, 1570824736, 2482111348, 2798323360, 17202377752, 24648077896, 52483285312, 56991483520, 90239155648, 139646736808 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Both the 3x+1 steps and the halving steps are counted.
Record values in A025586: a(n) = A025586(A006884(n)) and A025586(m) < a(n) for m < A006884(n). - Reinhard Zumkeller, May 11 2013
In an email of Aug 06 2023, Guy Chouraqui observes that the digital root of a(n) appears to be 7 for all n > 2. - N. J. A. Sloane, Aug 11 2023
REFERENCES
R. B. Banks, Slicing Pizzas, Racing Turtles and Further Adventures in Applied Mathematics, Princeton Univ. Press, 1999. See p. 96.
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..84 (from Eric Roosendaal's data)
Brian Hayes, Computer Recreations: On the ups and downs of hailstone numbers, Scientific American, 250 (No. 1, 1984), pp. 10-16.
J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
G. T. Leavens and M. Vermeulen, 3x+1 search programs, Computers and Mathematics with Applications, 24 (1992), 79-99. (Annotated scanned copy)
Eric Roosendaal, 3x+1 Path Records
MATHEMATICA
mcoll[n_]:=Max@@NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>=n&]; t={1, max=2}; Do[If[(y=mcoll[n])>max, AppendTo[t, max=y]], {n, 3, 10^6, 4}]; t (* Jayanta Basu, May 28 2013 *)
PROG
(Haskell)
a006885 = a025586 . a006884 -- Reinhard Zumkeller, May 11 2013
CROSSREFS
Sequence in context: A295906 A120948 A090453 * A220139 A027273 A210710
KEYWORD
nonn,nice
AUTHOR
STATUS
approved

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Last modified July 15 16:08 EDT 2024. Contains 374333 sequences. (Running on oeis4.)