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Numbers k whose Collatz sequence length is greater than k+1 (counting both the x/2 and the 3x+1 steps).
2

%I #19 Jul 16 2021 01:40:07

%S 3,6,7,9,11,14,15,18,19,27,31,41,47,54,55,62,63,71,73,82,83,91,94,95,

%T 97,108,109,110

%N Numbers k whose Collatz sequence length is greater than k+1 (counting both the x/2 and the 3x+1 steps).

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e a(1) is 3 because its Collatz sequence has eight steps: 3, 10, 5, 16, 8, 4, 2, 1.

%t Select[Range[1000], Length[Collatz[#]] > #+1 &] (* _T. D. Noe_, Aug 20 2013 *)

%Y Cf. A082984 (allows number of steps equal to n).

%K nonn,more

%O 1,1

%A _Gonzalo Ciruelos_, Aug 02 2013