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A261896 Consider the 2^n values of A162795(i)/i^2 for 2^n <= i < 2^(n+1); a(n) = value of i where this quantity is minimized.

%I A261896 #15 Feb 24 2021 02:48:19
%S A261896 3,5,11,25,43,89,179,361,727,1459,2921,5843,11689,23383,46769,93543,
%T A261896 187093,374193,748391,1496785,2993575,5987157,11974321,23948647,
%U A261896 47897299,95794607,191589221,383178449,766356903,1532713827,3065427663,6130855333,12261710675,24523421357,49046842723
%N A261896 Consider the 2^n values of A162795(i)/i^2 for 2^n <= i < 2^(n+1); a(n) = value of i where this quantity is minimized.
%C A261896 Sequence suggested by _Omar E. Pol_.
%C A261896 Note that all values in this sequence are odd and that a(n) is approximately 2*a(n-1).
%D A261896 D. Applegate, O. E. Pol and N. J. A. Sloane, The toothpick sequence and other sequences from cellular automata, Congressus Numerantium, v. 206 (2010) 157-191.
%H A261896 D. Applegate, O. E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The toothpick sequence and other sequences from cellular automata</a>; also available at <a href="http://arxiv.org/abs/1004.3036">arXiv:1004.3036v2</a>, [math.CO], 2010.
%H A261896 Steven R. Finch, <a href="/A139250/a139250_1.pdf">Toothpicks and Live Cells</a>, July 21, 2015. [Cached copy, with permission of the author]
%H A261896 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%t A261896 T = 1; t[0] = 0; t[1] = 1; lst = {1};
%t A261896 Do[twon = 2^n; Tmin = 1; imin = 1;
%t A261896     Do[If[i==twon, t[i]=twon,
%t A261896                    t[i]=2*t[i-twon]+t[i-twon+1];
%t A261896                    If[OddQ[i], T=T+t[i];
%t A261896                                Ttest=T/(i*i)];
%t A261896                                If[Ttest<Tmin, Tmin=Ttest; imin=i ]],
%t A261896       {i, twon, 2*twon - 1}];
%t A261896     AppendTo[lst, imin],
%t A261896     {n, 1, 15}];
%t A261896 lst
%t A261896 N[Tmin, 10]
%Y A261896 Cf. A139250, A147562, A162795, A170927, A195853, A260239, A261313, A261895.
%K A261896 nonn
%O A261896 0,1
%A A261896 _Robert Price_, Sep 05 2015