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A109734 In A109732, the number 2n+1 appears in position a(n).

%I A109734 #20 Mar 17 2019 03:24:52
%S A109734 1,2,5,3,30,6,28,4,38,26,11,7,36,29,14,8,201,39,34,27,180,12,175,9,
%T A109734 199,37,46,31,25,15,178,10,242,202,49,40,197,35,54,32,192,158,23,13,
%U A109734 208,176,57,16,240,200,61,41,83,47,195,33,121,42,67,17,190,179,70,18,689,243
%N A109734 In A109732, the number 2n+1 appears in position a(n).
%H A109734 N. J. A. Sloane and Alois P. Heinz, <a href="/A109734/b109734.txt">Table of n, a(n) for n = 0..20000</a> (first 1024 terms from N. J. A. Sloane)
%e A109734 9 appears in position 30 in A109732, so a(4) = 30.
%p A109734 with(LinearAlgebra);
%p A109734 hit:=Array(1..200000); a:=[1,3,7];
%p A109734 hit[1]:=1; hit[3]:=2; hit[7]:=3; S:={15}; L:=7;
%p A109734 for n from 4 to 20000 do
%p A109734 if (L mod 3 = 0) and hit[L/3]=0 then
%p A109734 L:=L/3; a:=[op(a),L]; hit[L]:=n; S:= S minus {L};
%p A109734    if hit[2*L+1]=0 then S:=S union {2*L+1}; fi;
%p A109734 else L:=min(S); a:=[op(a),L]; hit[L]:=n; S:=S minus {L};
%p A109734    if hit[2*L+1]=0 then S:=S union {2*L+1}; fi;
%p A109734 fi;
%p A109734 od:
%p A109734 #a;
%p A109734 w:=[];
%p A109734 for i from 0 to 50000 do
%p A109734 if hit[2*i+1]=0 then break; fi;
%p A109734 w:=[op(w),hit[2*i+1]]; od:
%p A109734 w; # _N. J. A. Sloane_, Aug 25 2015
%t A109734 (* using the M generated in A109732 *) ms=Sort[M]; k=1; While[ms[[k]]==2k-1, k++ ]; k=k-1; Take[Ordering[M], k] (* _T. D. Noe_, Aug 10 2005 *)
%Y A109734 Cf. A109732. For records see A109739 and A109740.
%K A109734 nonn
%O A109734 0,2
%A A109734 _N. J. A. Sloane_, Aug 10 2005
%E A109734 More terms from _T. D. Noe_ and _Ray Chandler_, Aug 10 2005