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%I #19 Feb 24 2021 02:48:19
%S 2,2,5,6,5,2,9,1,4,2
%N Decimal expansion of the lower limit of A162795(i)/i^2.
%C Sequence suggested by _Omar E. Pol_.
%C Similar to the constant mentioned in the Applegate-Pol-Sloane article, Section 5, the fractal-like structure. It is also mentioned in A139250 and A170927.
%C It appears that this sequence is a quarter of A261313 and half of A195853.
%D D. Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.], which is also available at <a href="http://arxiv.org/abs/1004.3036">arXiv:1004.3036v2</a>, [math.CO], 2010.
%H 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 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>
%e 0.2256529142...
%t T = 1; t[0] = 0; t[1] = 1; lst = {1};
%t Do[twon = 2^n; Tmin = 1; imin = 1;
%t Do[If[i == twon, t[i] = twon,
%t t[i] = 2*t[i - twon] + t[i - twon + 1];
%t If[OddQ[i], T = T + t[i];
%t Ttest = T/(i*i)];
%t If[ Ttest<imin, Tmin=Ttest; imin=i ]],
%t {i, twon, 2*twon - 1}];
%t AppendTo[lst, imin],
%t {n, 1, 15}];
%t lst
%t N[Tmin, 10]
%Y Cf. A139250, A147562, A162795, A170927, A195853, A260239, A261313, A261896.
%K nonn,cons,hard,more
%O 0,1
%A _Robert Price_, Sep 05 2015