%I #11 Mar 19 2021 00:11:55

%S 1,54,108,290,290,386,172146,298200,596400,596400,596400,795201,

%T 795201,2849196,2849196,8965036,33659819,45529226,52417676,93186987,

%U 104161282,104161282,104161282,436089218,436089218,605581697,934358530,934358530,934358530,3826876112

%N a(n) begins the first sequence of n consecutive positive integers with the same h-value and the same d-value in the Collatz (or '3x + 1') problem.

%C The Collatz function is as follows: F(x) = x/2 if x is even, otherwise F(x) = 3*x+1.

%C It is conjectured that starting from any number, and repeatedly applying the function on its previous result, we will always reach 1.

%C The d-value (or flight duration, A006577) is the number of steps needed to reach 1. The h-value (or flight height, A025586) is the maximum of the number's trajectory.

%H Guo-Gang Gao, <a href="http://dx.doi.org/10.1016/0012-365X(93)90240-T">On consecutive numbers of the same height in the Collatz problem</a>, Discrete Mathematics, Volume 112, pages 261-267, 1993.

%e a(3) = 108 because 108, 109 and 110 have same d-value (113) and same h-value (9232).

%e And 108 is the smallest number starting such sequence of 3 consecutive positive integers with same d-value and same h-value.

%Y Cf. A078441, A277109, A268253, A006577 (duration), A025586 (height), A056959.

%K nonn

%O 1,2

%A _Lamine Ngom_, Feb 10 2021