cp's OEIS Frontend

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

%I A308709 #42 Nov 03 2020 11:37:50
%S A308709 3,1,2,6,12,4,8,24,48,16,32,96,192,64,128,384,768,256,512,1536,3072,
%T A308709 1024,2048,6144,12288,4096,8192,24576,49152,16384,32768,98304,196608,
%U A308709 65536,131072,393216,786432,262144,524288,1572864,3145728,1048576
%N A308709 Start with 3, divide by 3, multiply by 2, multiply by 3, multiply by 2, repeat.
%C A308709 The division by 3 is always possible since it is always preceded by a multiplication by 3.
%C A308709 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.
%H A308709 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,4).
%F A308709 G.f.: x*(3+x+2*x^2+6*x^3)/(1-4*x^4).
%e A308709 3; /3 => 1; *2 => 2; *3 => 6;  *2 => 12;
%e A308709    /3 => 4; *2 => 8; *3 => 24; *2 => 48 ...
%t A308709 LinearRecurrence[{0, 0, 0, 4},{3, 1, 2, 6}, 50]
%o A308709 (Python 3)
%o A308709 def A308709List(init):
%o A308709     a = init
%o A308709     while True:
%o A308709         yield a
%o A308709         a //= 3
%o A308709         yield a
%o A308709         a <<= 1
%o A308709         yield a
%o A308709         a *= 3
%o A308709         yield a
%o A308709         a <<= 1
%o A308709 a = A308709List(3)
%o A308709 print([next(a) for _ in range(42)]) # _Peter Luschny_, Aug 05 2019
%Y A308709 Cf. A307407, A322469.
%K A308709 nonn,easy
%O A308709 1,1
%A A308709 _Georg Fischer_, Aug 05 2019