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Number of integers k < n whose Collatz (3x+1) trajectory contains n.
1

%I #11 Mar 01 2013 15:07:52

%S 0,0,0,1,1,0,0,4,0,4,2,0,3,1,0,11,4,0,0,9,0,5,1,0,0,9,0,2,2,0,1,1,0,

%T 11,5,0,0,2,0,25,1,0,0,6,0,5,3,0,1,1,0,23,9,0,0,3,0,7,1,0,6,3,0,2,2,0,

%U 2,1,0,14,7,0,0,4,0,7,1,0,0,19,0,2,2,0,1

%N Number of integers k < n whose Collatz (3x+1) trajectory contains n.

%C It is assumed that Collatz trajectory ends at 1.

%D R. K. Guy, Unsolved Problems in Number Theory, E16.

%H T. D. Noe, <a href="/A222617/b222617.txt">Table of n, a(n) for n = 1..10000</a>

%e a(8)=4, since 8 appears in Collatz trajectories of n < 8; similarly a(9)=0 since 9 does not appear in Collatz trajectories n < 9.

%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 100; t = Table[Collatz[n], {n, nn}]; Table[r = 0; Do[If[MemberQ[t[[i]], k], r++], {i, k - 1}]; r, {k, nn}] (* _T. D. Noe_, Feb 26 2013 *)

%Y Cf. A070165.

%K nonn

%O 1,8

%A _Jayanta Basu_, Feb 26 2013