A181171 Decimal expansion of the base x for which the double logarithm of 2 equals the natural log of 2, that is, log_x log_x 2 = log 2.

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Example

From R. J. Mathar, Oct 09 2010: (Start)
1.63662620778092377066392348972183502182...
log_(1.63662..)(2) = 1.4070142427036...
log_(1.63662..)(1.407014..) = A002162. (End)

Maple

f := log(log(2))/log(x)-log(log(x))/log(x)-log(2) ; fz := x-f/diff(f, x) ; z := 1.6 ; Digits := 120 ; for i from 1 to 10 do z := evalf(subs(x=z, fz)) ; print(%) ; end do: # R. J. Mathar, Oct 09 2010

Mathematica

RealDigits[ Exp[ ProductLog[Log[2]^2] / Log[2]], 10, 105][[1]] (* Jean-François Alcover, Jan 28 2014 *)

Crossrefs

Cf. A030797, which is the decimal expansion of the base n for which the double logarithm of e (log_n log_n e) = log e = 1, and which is the inverse of LambertW(1).

Sequence in context: A227400 A137245 A060294 * A193025 A021615 A198937

Adjacent sequences: A181168 A181169 A181170 * A181172 A181173 A181174

Keyword

nonn,cons

Author

Geoffrey Caveney, Oct 08 2010

Extensions

More digits from R. J. Mathar, Oct 09 2010

Status

approved