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

1,1

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.

Links

Table of n, a(n) for n=1..42.

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

Formula

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

Example

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

Mathematica

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

Prog

(Python 3)
def A308709List(init):
    a = init
    while True:
        yield a
        a //= 3
        yield a
        a <<= 1
        yield a
        a *= 3
        yield a
        a <<= 1
a = A308709List(3)
print([next(a) for _ in range(42)]) # Peter Luschny, Aug 05 2019

Crossrefs

Cf. A307407, A322469.

Sequence in context: A279859 A201655 A049917 * A166197 A010279 A024743

Adjacent sequences: A308706 A308707 A308708 * A308710 A308711 A308712

Keyword

nonn,easy

Author

Georg Fischer, Aug 05 2019

Status

approved