OFFSET
1,14
COMMENTS
Curiously, this constant is very close to 1 (up to a 10^-12 gap). This can be explained via the Dedekind eta function, after Steven Finch.
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 356.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Wikipedia, Radix tree
FORMULA
nu = 1/12 + Pi^2/(6*log(2)^2) + 2*sigma/log(2), where sigma = sum_{k=1..infinity} (-1)^k/(k*(2^k-1)).
EXAMPLE
1.000000000001237412575736110228719610646672874297732...
MATHEMATICA
digits = 103; sigma = NSum[(-1)^k/(k*(2^k-1)), {k, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> digits+10]; RealDigits[1/12 + Pi^2/(6*Log[2]^2) + 2*sigma/Log[2], 10, digits] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jul 29 2014
STATUS
approved