%I
%S 1,2,4,6,10,16,26,41,53,64,74,85,101,118,128,144,157,174,195,217,238,
%T 261,281,309,324
%N Number of distinct heights achieved in the Collatz (or '3x+1') problem when starting from numbers in the range [2^n,2^(n+1)).
%C Here the height is defined to be the number of halving and tripling steps required to reach 1.
%C Interestingly the values in this sequence grow slowly (almost linearly) indicating that the average number of starting values with the same height increases with n.
%C Question: Is this sequence always increasing?
%C Definition corrected by _N. J. A. Sloane_, Apr 09 2020. The old definition was "Number of unique heights achieved in the Collatz (or '3x+1') problem when starting from numbers in the range [2^n,2^(n+1))."
%e The heights for starting values 16 to 31 are: 4, 12, 20, 20, 7, 7, 15, 15, 10, 23, 10, 111, 18, 18, 18, 106. The unique heights are: 4, 12, 20, 7, 15, 10, 23, 111, 18, 106. Hence a(4)=10.
%Y Cf. A006577, A277109.
%K nonn
%O 0,2
%A _Dmitry Kamenetsky_, Jan 01 2017
