A308709 Start with 3, divide by 3, multiply by 2, multiply by 3, multiply by 2, repeat.

3, 1, 2, 6, 12, 4, 8, 24, 48, 16, 32, 96, 192, 64, 128, 384, 768, 256, 512, 1536, 3072, 1024, 2048, 6144, 12288, 4096, 8192, 24576, 49152, 16384, 32768, 98304, 196608, 65536, 131072, 393216, 786432, 262144, 524288, 1572864, 3145728, 1048576

Offset: 1

Author

Georg Fischer, Aug 05 2019

Keywords

• nonn
• easy

Comments

The division by 3 is always possible since it is always preceded by a multiplication by 3.

This sequence arises in the "3x+1" (Collatz) problem. In the rows of A322469, the terms of this sequence appear at the end of any first row which is longer than all previous rows.

Examples

			3; /3 => 1; *2 => 2; *3 => 6;  *2 => 12;
   /3 => 4; *2 => 8; *3 => 24; *2 => 48 ...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,4).

Crossrefs

Cf. A307407, A322469.

Programs

Mathematica

LinearRecurrence[{0, 0, 0, 4},{3, 1, 2, 6}, 50]

Formula

G.f.: x*(3+x+2*x^2+6*x^3)/(1-4*x^4).