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%I #16 Sep 22 2013 15:44:02
%S 3,7,9,15,19,25,33,39,51,91,121,159,166,183,243,250,333,376,411,432,
%T 487,501,649,667,865,889,975,1153,1185,1299,1335,1731,1779,2307,3643,
%U 4857,7287
%N Numbers n such that the trajectory of n under the "3x+1" map reaches n+1.
%C 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).
%C There are no more terms < 10^9. - _Donovan Johnson_, Sep 22 2013
%e 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.
%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[100000], MemberQ[Collatz[#], # + 1] &] (* _T. D. Noe_, Feb 22 2013 *)
%o (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,","); ); ))
%Y Cf. A070165 (Collatz trajectories), A221213, A222293, A070991.
%K nonn
%O 1,1
%A _Benoit Cloitre_ and Boris Gourevitch (boris(AT)pi314.net), May 18 2002
%E Corrected by _T. D. Noe_, Oct 25 2006
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