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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)
14
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.

REFERENCES

T. Ahmed, H. Snevily, Are there an infinite number of Collatz integers?, http://users.encs.concordia.ca/~ta_ahmed/collatz.pdf, 2013.

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, Table of n, a(n) for n = 1..130 (from Eric Roosendaal's data)

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

R. Munafo, Integer Sequences Related to 3x+1 Collatz Iteration

Eric Roosendaal, 3x+1 Delay Records

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

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

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-Fran├žois Alcover, Feb 14 2012 *)

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 * A208892 A085397 A073439

Adjacent sequences:  A006874 A006875 A006876 * A006878 A006879 A006880

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Robert Munafo

STATUS

approved

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Last modified October 24 06:31 EDT 2014. Contains 248502 sequences.