login
A070993
Numbers n such that the trajectory of n under the "3x+1" map reaches n+1.
6
3, 7, 9, 15, 19, 25, 33, 39, 51, 91, 121, 159, 166, 183, 243, 250, 333, 376, 411, 432, 487, 501, 649, 667, 865, 889, 975, 1153, 1185, 1299, 1335, 1731, 1779, 2307, 3643, 4857, 7287
OFFSET
1,1
COMMENTS
From Collatz conjecture, the trajectory of n never reaches n again. Is this sequence finite? (it seems there are no further terms below 10^6).
There are no more terms < 10^9. - Donovan Johnson, Sep 22 2013
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) which contains 39+1=40, so 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 22 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, ", "); ); ))
CROSSREFS
Cf. A070165 (Collatz trajectories), A221213, A222293, A070991.
Sequence in context: A104177 A099204 A219608 * A261524 A261871 A191131
KEYWORD
nonn
AUTHOR
Benoit Cloitre and Boris Gourevitch (boris(AT)pi314.net), May 18 2002
EXTENSIONS
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved