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

1,2

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.

Links

Table of n, a(n) for n=1..54.

Example

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

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 *)

Crossrefs

Cf. A000079, A181762.

Sequence in context: A071601 A114400 A341742 * A023898 A125853 A080025

Adjacent sequences: A330707 A330708 A330709 * A330711 A330712 A330713

Keyword

nonn

Author

Cara Bennett, Dec 27 2019

Status

approved