

A070993


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


3



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
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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


LINKS

Table of n, a(n) for n=1..37.


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==n1, print1(n, ", "); ); ))


CROSSREFS

Cf. A070165 (Collatz trajectories), A221213, A222293, A070991.
Sequence in context: A104177 A099204 A219608 * A261524 A261871 A191131
Adjacent sequences: A070990 A070991 A070992 * A070994 A070995 A070996


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



