%I A109732
%S A109732 1,3,7,15,5,11,23,31,47,63,21,43,87,29,59,95,119,127,175,191,239,255,85,
%T A109732 171,57,19,39,13,27,9,55,79,111,37,75,25,51,17,35,71,103,115,143,151,
%U A109732 159,53,107,207,69,139,215,223,231,77,155,279,93,187,287,303,101,203
%N A109732 a(1) = 1; for n>1, a(n) is the smallest number not already present which 
               is entailed by the rules (i) k present => 2k+1 present; (ii) 3k present 
               => k present.
%C A109732 Van der Poorten asks if every odd number is in the sequence. This seems 
               very likely.
%C A109732 Odd numbers of the form 2^k+1 take a long time to appear; e.g. 2^12+1 
               appears at a(64607). - T. D. Noe (noe(AT)sspectra.com), Aug 10 2005
%H A109732 T. D. Noe, <a href="b109732.txt">Table of n, a(n) for n=1..1000</a>
%H A109732 T. D. Noe, <a href="A109732.gif">Graph of first 1000 terms</a>
%t A109732 maxVal=1000; f[n_]:=Module[{lst={}, x=n}, While[x=2x+1; x<maxVal, AppendTo[lst, 
               x]]; lst]; M={1}; pending=f[1]; While[Length[pending]>0, next=First[pending]; 
               pending=Rest[pending]; If[ !MemberQ[M, next], AppendTo[M, next]; 
               While[Mod[next, 3]==0 && !MemberQ[M, next/3], next=next/3; AppendTo[M, 
               next]; pending=Union[pending, f[next]]]]]; M (Noe)
%Y A109732 Sequence in context: A128658 A001203 A154883 this_sequence A114396 A102032 
               A086517
%Y A109732 Adjacent sequences: A109729 A109730 A109731 this_sequence A109733 A109734 
               A109735
%K A109732 nonn,easy
%O A109732 1,2
%A A109732 N. J. A. Sloane (njas(AT)research.att.com), prompted by a posting by 
               Alf van der Poorten (alf(AT)math.mq.edu.au) to the Number Theory 
               List, Aug 10 2005
%E A109732 More terms from T. D. Noe (noe(AT)sspectra.com), Aug 10 2005