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%I #12 Jan 10 2020 12:35:08
%S 1,2,4,8,9,16,18,32,36,41,53,64,69,72,82,106,107,111,128,138,141,143,
%T 144,163,164,169,189,212,214,217,219,222,231,247,256,263,276,281,282,
%U 286,287,288,299,326,328,331,338,349,363,373,378,381,383,397
%N Numbers that reach 1 in the 3x + 5 variation of Collatz map.
%C In this variation of the Collatz function, f(x) = x/2 if x is even, 3x + 5 if x is odd.
%C f(a(n)) will end in the loop 8, 4, 2, 1.
%C For any odd number n in the sequence, n*2^x where x is a positive integer will also be in the sequence.
%e For n = 53, the numbers produced are 53 -> 164 -> 82 -> 41 -> 128 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1 -> 8 -> 4 -> 2 -> 1 -> ...
%t Select[Range@ 400, Function[n, NestWhile[If[EvenQ@ #, #/2, 3 # + 5] &, n, And[FreeQ[{##}, 1], Count[{##}, n] <= 2] &, All, 120] == 1]] (* _Michael De Vlieger_, Dec 27 2019 *)
%Y Cf. A000079, A181762.
%K nonn
%O 1,2
%A _Cara Bennett_, Dec 27 2019