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A308709
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Start with 3, divide by 3, multiply by 2, multiply by 3, multiply by 2, repeat.
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2
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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
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f.: x*(3+x+2*x^2+6*x^3)/(1-4*x^4).
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EXAMPLE
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3; /3 => 1; *2 => 2; *3 => 6; *2 => 12;
/3 => 4; *2 => 8; *3 => 24; *2 => 48 ...
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 4}, {3, 1, 2, 6}, 50]
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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