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 A006877 In the '3x+1' problem, these values for the starting value set new records for number of steps to reach 1. (Formerly M0748) 28
 1, 2, 3, 6, 7, 9, 18, 25, 27, 54, 73, 97, 129, 171, 231, 313, 327, 649, 703, 871, 1161, 2223, 2463, 2919, 3711, 6171, 10971, 13255, 17647, 23529, 26623, 34239, 35655, 52527, 77031, 106239, 142587, 156159, 216367, 230631, 410011, 511935, 626331, 837799 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Both the 3x+1 steps and the halving steps are counted. This sequence without a(2) = 2 specifies where records occur in A208981. - Omar E. Pol, Apr 14 2022 REFERENCES Gonnet, Gaston H. "Computations on the 3n+1 conjecture." Maple Technical Newsletter 6 (1991): 18-22. 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 T. D. Noe, Table of n, a(n) for n = 1..130 (from Eric Roosendaal's data) T. Ahmed, H. Snevily, Are there an infinite number of Collatz integers?, 2013. 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 Delay 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 MAPLE A006877 := proc(n) local a, L; L := 0; a := n; while a <> 1 do if a mod 2 = 0 then a := a/2; else a := 3*a+1; fi; L := L+1; od: RETURN(L); end; MATHEMATICA numberOfSteps[x0_] := Block[{x = x0, nos = 0}, While [x != 1 , If[Mod[x, 2] == 0 , x = x/2, x = 3*x + 1]; nos++]; nos]; a[1] = 1; a[n_] := a[n] = Block[{x = a[n-1] + 1}, record = numberOfSteps[x - 1]; While[ numberOfSteps[x] <= record, x++]; x]; A006877 = Table[ Print[a[n]]; a[n], {n, 1, 44}](* Jean-François Alcover, Feb 14 2012 *) DeleteDuplicates[Table[{n, Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]]}, {n, 838000}], GreaterEqual[#1[[2]], #2[[2]]]&][[All, 1]] (* Harvey P. Dale, May 13 2022 *) PROG (PARI) A006577(n)=my(s); while(n>1, n=if(n%2, 3*n+1, n/2); s++); s step(n, r)=my(t); forstep(k=bitor(n, 1), 2*n, 2, t=A006577(k); if(t>r, return([k, t]))); [2*n, r+1] r=0; print1(n=1); for(i=1, 100, [n, r]=step(n, r); print1(", "n)) \\ Charles R Greathouse IV, Apr 01 2013 CROSSREFS Cf. A006884, A006885, A006877, A006878, A033492. Sequence in context: A018700 A018295 A033495 * A328832 A263881 A208892 Adjacent sequences: A006874 A006875 A006876 * A006878 A006879 A006880 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)