cp's OEIS Frontend

A308712 a(0) = 0 and a(1) = 1; for n > 1, a(n) = a(n-1)/2 if that number is an integer and not already in the sequence, otherwise a(n) = 3*a(n-1) + remainder of a(n-1)/2. (A variant of the Collatz sequence).

%I A308712 #30 Jan 03 2021 09:56:56
%S A308712 0,1,4,2,6,3,10,5,16,8,24,12,36,18,9,28,14,7,22,11,34,17,52,26,13,40,
%T A308712 20,60,30,15,46,23,70,35,106,53,160,80,240,120,360,180,90,45,136,68,
%U A308712 204,102,51,154,77,232,116,58,29,88,44,132,66,33,100,50,25,76,38,19,58
%N A308712 a(0) = 0 and a(1) = 1; for n > 1, a(n) = a(n-1)/2 if that number is an integer and not already in the sequence, otherwise a(n) = 3*a(n-1) + remainder of a(n-1)/2.  (A variant of the Collatz sequence).
%C A308712 Similar to A128333 and related to the 3x+1 (Collatz) sequence. Hits all positive integers?
%H A308712 Rémy Sigrist, <a href="/A308712/b308712.txt">Table of n, a(n) for n = 0..10000</a>
%e A308712 a(1)=1 => a(2)=3*1+1=4 because a(1) is odd => a(3)=4/2=2 because a(2) is even => a(4)=3*2+0=6 because a(3) is even but a(3)/2 is already in the sequence.
%t A308712 a[0] = 0; a[1] = 1; a[n_] := a[n] = With[{b = a[n-1]}, If[EvenQ[b] && FreeQ[Array[a, n, 0], b/2], b/2, 3 b + Mod[b, 2]]];
%t A308712 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jun 20 2019 *)
%Y A308712 Cf. A126038, A005132, A128333.
%K A308712 easy,nonn
%O A308712 0,3
%A A308712 _Alexis Monnerot-Dumaine_, Jun 19 2019