

A308709


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


2



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
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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)/(14*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



