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

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]]

Crossrefs

Cf. A072449, A276521, A276538, A276539, A277313, A278812, A283749.

Sequence in context: A033259 A212298 A064926 * A154006 A143080 A011484

Adjacent sequences: A285811 A285812 A285813 * A285815 A285816 A285817

Keyword

nonn,cons

Author

Alex Klotz and Robert G. Wilson v, Apr 27 2017

Status

approved