A285814 - OEIS

A285814

Decimal expansion of the limit of the nested logarithm log(1+2*log(1+3*log(1+4*log(...)))).

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

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OFFSET

1,2

COMMENTS

No closed form expression is known. Probably transcendental but this is unproved.

LINKS

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

Alex Klotz, The Nested Logarithm Constants

EXAMPLE

1.6630272645956895211326676626846841888930929806388191033183243319627019656...

MATHEMATICA

bgn = 147; RealDigits[ Fold[ N[1 + #2*Log@#1, 200] &, bgn +1, Reverse@Range@bgn] -1, 10, 111][[1]]