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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. 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..94 (first 89 terms from T. D. Noe and 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 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 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 (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. Cf. A006885, A006877, A006878, A033492, A060412-A060415, A132348. Sequence in context: A209658 A098763 A001276 * A074742 A020873 A049958 Adjacent sequences: A006881 A006882 A006883 * A006885 A006886 A006887 KEYWORD nonn,nice AUTHOR EXTENSIONS b-file extended by N. J. A. Sloane, Nov 27 2007 STATUS approved

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Last modified February 6 13:25 EST 2023. Contains 360110 sequences. (Running on oeis4.)