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A277435
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Decimal expansion of lim_{n->inf} (2 - sqrt(2)^^n)/log(2)^n, where x^^n denotes tetration.
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5
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6, 3, 2, 0, 9, 8, 6, 6, 1, 0, 5, 0, 8, 2, 9, 2, 5, 0, 3, 5, 5, 4, 5, 0, 6, 4, 5, 9, 9, 0, 7, 8, 0, 8, 6, 2, 7, 9, 9, 4, 7, 4, 5, 5, 2, 3, 2, 4, 1, 6, 4, 4, 7, 9, 6, 6, 9, 7, 2, 3, 3, 8, 2, 4, 3, 2, 5, 8, 6, 1, 6, 2, 7, 6, 1, 5, 0, 9, 6, 2, 1, 4, 7, 0, 9, 1, 7, 6, 6, 4, 9, 4, 2, 6, 6, 7, 7, 3, 7, 1, 6, 3, 7, 9, 4, 6
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OFFSET
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0,1
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COMMENTS
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Tetration x^^n is defined recursively: x^^0 = 1, x^^n = x^(x^^(n-1)). Note that sqrt(2)^^inf = lim_{n->inf} sqrt(2)^^n = 2. Asymptotically, sqrt(2)^^n = 2 - O(log(2)^n). This constant is the coefficient in the O(log(2)^n) term. Furthermore, sqrt(2)^^n = 2 - a*log(2)^n + (a^2/(4*(1 - 1/log(2))))*log(2)^(2*n) + O(log(2)^(3*n)).
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LINKS
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Table of n, a(n) for n=0..105.
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Tetration
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FORMULA
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a = 2*sqrt(2)*A260691/(1-log(2)).
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EXAMPLE
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0.63209866105082925035545064599078...
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MATHEMATICA
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RealDigits[SequenceLimit[1`200 Table[(2 - Power @@ Table[Sqrt[2], {n}])/Log[2]^n, {n, 1, 200}]], 10, 100][[1]]
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CROSSREFS
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Cf. A198094, A260691.
Sequence in context: A108451 A122178 A126445 * A033326 A068996 A068924
Adjacent sequences: A277432 A277433 A277434 * A277436 A277437 A277438
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KEYWORD
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nonn,cons
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AUTHOR
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Vladimir Reshetnikov, Oct 14 2016
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STATUS
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approved
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