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A280918 2nd term of the continued fraction for 2-sqrt(2)^^n, where x^^n denotes tetration. 1
1, 2, 4, 6, 9, 13, 20, 29, 42, 61, 88, 128, 184, 267, 385, 556, 803, 1159, 1672, 2413, 3481, 5023, 7247, 10456, 15085, 21764, 31399, 45299, 65354, 94286, 136026, 196245, 283122, 408459, 589282, 850155, 1226515, 1769487, 2552830, 3682956, 5313383, 7665592 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Tetration x^^n is defined recursively: x^^0 = 1, x^^n = x^(x^^(n-1)). Note that lim_{n->inf} sqrt(2)^^n = 2. This sequence shows the speed of convergence to this limit.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..300

Eric Weisstein's World of Mathematics, Power Tower

Wikipedia, Tetration

FORMULA

a(n) ~ 1/(A277435*log(2)^n).

MATHEMATICA

Table[ContinuedFraction[2 - Power@@Table[Sqrt[2], {n}], 2][[2]], {n, 42}]

CROSSREFS

Cf. A198094, A277435.

Sequence in context: A081659 A143586 A241546 * A081225 A164140 A205883

Adjacent sequences:  A280915 A280916 A280917 * A280919 A280920 A280921

KEYWORD

nonn

AUTHOR

Vladimir Reshetnikov, Jan 10 2017

STATUS

approved

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)