A070991 Numbers n such that the trajectory of n under the `3x+1' map reaches n - 1.

2, 3, 5, 6, 9, 11, 14, 17, 18, 39, 41, 47, 54, 57, 59, 62, 71, 81, 89, 107, 108, 161, 252, 284, 378, 639, 651, 959, 977, 1368, 1439, 1823, 2159, 2430, 2735, 3239, 4103, 4617, 4859, 6155, 7289, 9233

Offset

1,1

Comments

From Collatz conjecture, the trajectory of n never reaches n again. Is this sequence finite?

There are no more terms < 10^9. - Donovan Johnson, Sep 22 2013

Links

Table of n, a(n) for n=1..42.

Example

Trajectory of 39 is: (118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) and 39-1 = 38 is reached, hence 39 is in the sequence.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[100000], MemberQ[Collatz[#], # - 1] &] (* T. D. Noe, Feb 21 2013 *)

Prog

(PARI) for(n=1, 10000, s=n; t=0; while(s!=1, t++; if(s%2==0, s=s/2, s=3*s+1); if(s==n-1, print1(n, ", "); ); ))
(Haskell)
a070991 n = a070991_list !! (n-1)
a070991_list = filter (\x -> (x - 1) `elem` a070165_row x) [1..]
-- Reinhard Zumkeller, Feb 22 2013

Crossrefs

Cf. A070165 (Collatz trajectories), A219696, A221213, A070993.

Sequence in context: A355616 A046657 A102825 * A225527 A008747 A327516

Adjacent sequences: A070988 A070989 A070990 * A070992 A070993 A070994

Keyword

easy,nonn

Author

Benoit Cloitre and Boris Gourevitch (boris(AT)pi314.net), May 18 2002

Status

approved