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A181171
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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.
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0
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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
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..105.
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EXAMPLE
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From R. J. Mathar, Oct 09 2010: (Start)
1.63662620778092377066392348972183502182...
log_(1.63662..)(2) = 1.4070142427036...
log_(1.63662..)(1.407014..) = A002162. (End)
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MAPLE
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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
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MATHEMATICA
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RealDigits[ Exp[ ProductLog[Log[2]^2] / Log[2]], 10, 105][[1]] (* Jean-François Alcover, Jan 28 2014 *)
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CROSSREFS
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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
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KEYWORD
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nonn,cons
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AUTHOR
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Geoffrey Caveney, Oct 08 2010
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EXTENSIONS
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More digits from R. J. Mathar, Oct 09 2010
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STATUS
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approved
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