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A006884 In the `3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1.
(Formerly M0843)
23
1, 2, 3, 7, 15, 27, 255, 447, 639, 703, 1819, 4255, 4591, 9663, 20895, 26623, 31911, 60975, 77671, 113383, 138367, 159487, 270271, 665215, 704511, 1042431, 1212415, 1441407, 1875711, 1988859, 2643183, 2684647, 3041127, 3873535, 4637979, 5656191 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Where records occur in A025586: A006885(n) = A025586(a(n)) and A025586(m) < A006885(n) for m < a(n). - Reinhard Zumkeller, May 11 2013

REFERENCES

R. B. Banks, Slicing Pizzas, Racing Turtles and Further Adventures in Applied Mathematics, Princeton Univ. Press, 1999. See p. 96.

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 and N. J. A. Sloane, Table of n, a(n) for n=1..89 (from Eric Roosendaal's data, supplemented by further values from the web page of Tomas Oliveira e Silva)

J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.

Tomas Oliveira e Silva, Tables (gives many more terms)

Eric Roosendaal, 3x+1 Path Records

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

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

MATHEMATICA

mcoll[n_]:=Max@@NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; t={1, max=2}; Do[If[(y=mcoll[n])>max, max=y; AppendTo[t, n]], {n, 3, 705000, 4}]; t (* Jayanta Basu, May 28 2013 *)

PROG

(Haskell)

a006884 n = a006884_list !! (n-1)

a006884_list = f 1 0 a025586_list where

   f i r (x:xs) = if x > r then i : f (i + 1) x xs else f (i + 1) r xs

-- Reinhard Zumkeller, May 11 2013

CROSSREFS

A060409 gives associated "dropping times", A060410 the maximal values and A060411 the steps at which the maxima occur.

Cf. A006885, A006877, A006878, A033492, A060412-A060415, A132348.

Sequence in context: A066044 A066460 A001276 * A074742 A020873 A049958

Adjacent sequences:  A006881 A006882 A006883 * A006885 A006886 A006887

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Robert Munafo

EXTENSIONS

b-file extended by N. J. A. Sloane, Nov 27 2007

STATUS

approved

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Last modified November 21 21:29 EST 2014. Contains 249791 sequences.