A330710 Numbers that reach 1 in the 3x + 5 variation of Collatz map.

1, 2, 4, 8, 9, 16, 18, 32, 36, 41, 53, 64, 69, 72, 82, 106, 107, 111, 128, 138, 141, 143, 144, 163, 164, 169, 189, 212, 214, 217, 219, 222, 231, 247, 256, 263, 276, 281, 282, 286, 287, 288, 299, 326, 328, 331, 338, 349, 363, 373, 378, 381, 383, 397

Offset: 1

Author

Cara Bennett, Dec 27 2019

Keywords

• nonn

Comments

In this variation of the Collatz function, f(x) = x/2 if x is even, 3x + 5 if x is odd.

f(a(n)) will end in the loop 8, 4, 2, 1.

For any odd number n in the sequence, n*2^x where x is a positive integer will also be in the sequence.

Examples

			For n = 53, the numbers produced are 53 -> 164 -> 82 -> 41 -> 128 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1 -> 8 -> 4 -> 2 -> 1 -> ...
		

Crossrefs

Cf. A000079, A181762.

Programs

Mathematica

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 *)