A006885 Record highest point of trajectory before reaching 1 in '3x+1' problem, corresponding to starting values in A006884. (Formerly M2086)

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

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)

Peter Munn, Plot2 graph of record highest point against starting value

Eric Roosendaal, 3x+1 Path Records

Robert G. Wilson v, Letter to N. J. A. Sloane with attachments, Jan. 1989

Robert G. Wilson v, Tables of A6877, A6884, A6885, Jan. 1989

Index entries for sequences from "Goedel, Escher, Bach"

Index entries for sequences related to 3x+1 (or Collatz) problem

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

Cf. A006884, A006877, A006878, A033492.

Sequence in context: A295906 A120948 A090453 * A220139 A027273 A210710

Adjacent sequences: A006882 A006883 A006884 * A006886 A006887 A006888

Keyword

nonn,nice

Author

Robert Munafo

Status

approved