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

Author

Geoffrey Caveney, Oct 08 2010

Keywords

• nonn
• cons

Examples

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

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).

Programs

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 *)

Extensions

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