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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)
24
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.
D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
David Barina, Table of n, a(n) for n = 1..97 (terms 1..84 from T. D. Noe, terms 85..89 from N. J. A. Sloane)
David Barina, Path records.
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 problems, Computers and Mathematics with Applications, 24 (1992), 79-99.
G. T. Leavens and M. Vermeulen, 3x+1 search programs, Computers and Mathematics with Applications, 24 (1992), 79-99. (Annotated scanned copy)
Tomás Oliveira e Silva, Tables (gives many more terms).
Eric Roosendaal, 3x+1 Path Records.
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 *)
DeleteDuplicates[Parallelize[Table[{n, Max[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]]}, {n, 57*10^5}]], GreaterEqual[#1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Apr 23 2023 *)
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
(PARI) A025586(n)=my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n)); n>>=1); r
r=0; for(n=1, 1e6, t=A025586(n); if(t>r, r=t; print1(n", "))) \\ Charles R Greathouse IV, May 25 2016
CROSSREFS
A060409 gives associated "dropping times", A060410 the maximal values and A060411 the steps at which the maxima occur.
Sequence in context: A209658 A098763 A001276 * A074742 A020873 A049958
KEYWORD
nonn,nice
AUTHOR
STATUS
approved

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Last modified May 25 06:28 EDT 2024. Contains 372782 sequences. (Running on oeis4.)