

A260691


Decimal expansion of a constant related to asymptotic behavior of superroots of 2: lim_{n>inf} (sr[n](2)  sqrt(2))/log(2)^n.


5



0, 6, 8, 5, 7, 5, 6, 5, 9, 8, 1, 1, 3, 2, 9, 1, 0, 3, 9, 7, 6, 5, 5, 3, 3, 1, 1, 4, 1, 5, 5, 0, 6, 5, 5, 4, 2, 3, 3, 5, 6, 3, 5, 7, 1, 3, 7, 8, 6, 1, 9, 4, 4, 7, 4, 6, 8, 1, 2, 5, 1, 7, 0, 5, 1, 0, 3, 4, 8, 4, 4, 6, 8, 0, 7, 3, 4, 9, 7, 3, 7, 7, 4, 6, 0, 7, 1, 7, 1, 4, 3, 0, 9, 3, 0, 8, 1, 9, 7, 9, 1, 1, 1, 3, 9, 7, 4, 2, 8, 6
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OFFSET

0,2


COMMENTS

Tetration is defined recursively: x^^0 = 1, x^^n = x^(x^^(n1)). Its inverse, superroot, is defined: sr[n](y) = x iff x^^n = y. Note that lim_{n>inf} sr[n](2) = sqrt(2). Asymptotically, sr[n](2) = sqrt(2) + O(log(2)^n). This constant is the coefficient in the O(log(2)^n) term, i.e. lim_{n>inf} (sr[n](2)  sqrt(2))/log(2)^n.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..193
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Superroot


FORMULA

a = A277435*(1log(2))/(2*sqrt(2)).  Vladimir Reshetnikov, Oct 18 2016


EXAMPLE

0.0685756598113291039765533114155...


MATHEMATICA

{0}~Join~RealDigits[SequenceLimit[1`200 Table[(2  Power @@ Table[Sqrt[2], {n}])/Log[2]^n, {n, 1, 200}]] (1  Log[2])/(2 Sqrt[2]), 10, 100][[1]] (* Vladimir Reshetnikov, Oct 18 2016 *)


CROSSREFS

Cf. A198094, A277435.
Sequence in context: A296426 A249282 A289090 * A296845 A030644 A319032
Adjacent sequences: A260688 A260689 A260690 * A260692 A260693 A260694


KEYWORD

cons,nonn


AUTHOR

Vladimir Reshetnikov, Nov 15 2015


STATUS

approved



