A070993 Numbers n such that the trajectory of n under the "3x+1" map reaches n+1.

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

Author

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

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A070165 (Collatz trajectories), A221213, A222293, A070991.

Programs

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[100000], MemberQ[Collatz[#], # + 1] &] (* T. D. Noe, Feb 22 2013 *)

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,","); ); ))

Extensions

Corrected by T. D. Noe, Oct 25 2006