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A170927 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. 6
1, 2, 5, 12, 21, 44, 89, 180, 362, 728, 1459, 2921, 5843, 11690, 23384, 46770, 93544, 187094, 374193, 748391, 1496786, 2993576, 5987158, 11974321, 23948647, 47897300, 95794608, 191589222, 383178450, 766356910, 1532713828, 3065427664, 6130855333, 12261710675 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

{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.

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

LINKS

Robert Price, Table of n, a(n) for n = 0..169

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

Steven R. Finch, Toothpicks and Live Cells, July 21, 2015. [Cached copy, with permission of the author]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

EXAMPLE

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.

CROSSREFS

Cf. A139250, A170927, A147562, A260239, A261313.

Sequence in context: A182993 A238741 A218904 * A182201 A106331 A116727

Adjacent sequences:  A170924 A170925 A170926 * A170928 A170929 A170930

KEYWORD

nonn

AUTHOR

Benoit Jubin, Jan 22 2010, Feb 06 2010

EXTENSIONS

a(26)-a(33) from Robert Price, Aug 18 2012

STATUS

approved

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Last modified February 19 14:42 EST 2018. Contains 299334 sequences. (Running on oeis4.)