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%I #17 May 25 2022 02:26:09
%S 1,2,6,65,673,342,2919,129991,1590511,301695657,1412987847
%N Smallest number that requires n^3 steps to reach 1 in its Collatz trajectory (counting x/2 and 3x+1 steps).
%C a(11) > 7*10^11. - _Donovan Johnson_
%D R. K. Guy, Problem E16, Unsolved Problems in Number Theory, 2nd edition, Springer-Verlag, NY pp. 215-218
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F Mapping at each step for Collatz problem: x -> x/2 if n is even, else x -> 3*x+1; count the steps until x=1.
%e a(2) = 6 since the trajectory of 6 requires 2^3 = 8 steps to reach 1 (the trajectory is 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1), and 6 is the smallest number for which this is the case.
%Y Cf. A006577, A066773.
%K nonn,more
%O 0,2
%A _Randall L Rathbun_, Jan 18 2002
%E More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2002
%E a(10) from _Donovan Johnson_, Nov 13 2010
%E Edited by _Jon E. Schoenfield_, Jan 28 2014
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