A280918 2nd term of the continued fraction for 2-sqrt(2)^^n, where x^^n denotes tetration.

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

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: A344677 A241546 A370320 * A081225 A164140 A205883

Adjacent sequences: A280915 A280916 A280917 * A280919 A280920 A280921

Keyword

nonn

Author

Vladimir Reshetnikov, Jan 10 2017

Status

approved