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%I #18 Sep 22 2013 16:03:33
%S 2,3,5,6,9,11,14,17,18,39,41,47,54,57,59,62,71,81,89,107,108,161,252,
%T 284,378,639,651,959,977,1368,1439,1823,2159,2430,2735,3239,4103,4617,
%U 4859,6155,7289,9233
%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?
%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) and 39-1 = 38 is reached, hence 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 21 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,","); ); ))
%o (Haskell)
%o a070991 n = a070991_list !! (n-1)
%o a070991_list = filter (\x -> (x - 1) `elem` a070165_row x) [1..]
%o -- _Reinhard Zumkeller_, Feb 22 2013
%Y Cf. A070165 (Collatz trajectories), A219696, A221213, A070993.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_ and Boris Gourevitch (boris(AT)pi314.net), May 18 2002
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