A225092 Decimal expansion of (-1)*lim_{k->inf} log^k(2^^k), where log^k(x) denotes repeated natural logarithm log(log(...(log(x)))) with k log's and 2^^k denotes a power tower 2^2^...^2 with k 2's.

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

Offset

0,2

Comments

The sequence log^k(2^^k) converges extremely fast to the limiting value -0.146262291239074020528091308030992016863490703821292...

The difference between 6th and 7th terms < 10^-19734.

Links

Table of n, a(n) for n=0..129.

Eric Weisstein's World of Mathematics, Power Tower

Wikipedia, Tetration

Mathematica

N[Log[Log[Log[Log[Log[2^65536 Log[2] + Log[Log[2]]]]]]], 130]

Prog

(PARI) log(log(log(log(log(log(2)<<65536+log(log(2))))))) \\ Charles R Greathouse IV, Apr 29 2013

Crossrefs

Sequence in context: A244993 A160502 A010669 * A029677 A045867 A236189

Adjacent sequences: A225089 A225090 A225091 * A225093 A225094 A225095

Keyword

nonn,cons,easy

Author

Vladimir Reshetnikov, Apr 29 2013

Status

approved