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%I #24 Feb 24 2021 02:48:19
%S 1,2,5,12,21,44,89,180,362,728,1459,2921,5843,11690,23384,46770,93544,
%T 187094,374193,748391,1496786,2993576,5987158,11974321,23948647,
%U 47897300,95794608,191589222,383178450,766356910,1532713828,3065427664,6130855333,12261710675
%N Consider the 2^n values of A139250(i)/i^2 for 2^n <= i < 2^(n+1); a(n) = value of i where this quantity is minimized.
%C {log_2 a(n)} converges to about 0.513441 and equivalently 2^{log_2 a(n)}-1 converges to about 1.427451, and the corresponding values T(i)/i^2 converge to about 0.4513058.
%C For all values listed, a(n) = 2 * a(n-1) + c(n), where c(n) is a small positive integer, except for a(4) where c(4)=-3. - _Robert Price_, Aug 16 2015
%H Robert Price, <a href="/A170927/b170927.txt">Table of n, a(n) for n = 0..169</a>
%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.]
%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 The values of A139250(i)/i^2 for i = 1 .., 15 are 1.0, 0.7500000000, 0.7777777778, 0.6875000000, 0.6000000000, 0.6388888889, 0.7142857143, 0.6718750000, 0.5802469136, 0.5500000000, 0.5537190083, 0.5486111111, 0.5621301775, 0.6275510204, 0.6888888889, 0.6679687500. The minimal value for 4 <= i <= 7 is 0.6000000000 at i=5.
%Y Cf. A139250, A170927, A147562, A260239, A261313.
%K nonn
%O 0,2
%A _Benoit Jubin_, Jan 22 2010, Feb 06 2010
%E a(26)-a(33) from _Robert Price_, Aug 18 2012
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