login
A245675
Decimal expansion of 'nu', a coefficient related to the variance for searching corresponding to patricia tries.
3
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 7, 4, 1, 2, 5, 7, 5, 7, 3, 6, 1, 1, 0, 2, 2, 8, 7, 1, 9, 6, 1, 0, 6, 4, 6, 6, 7, 2, 8, 7, 4, 2, 9, 7, 7, 3, 2, 0, 4, 8, 1, 9, 6, 5, 4, 8, 4, 4, 3, 8, 4, 4, 1, 7, 1, 8, 2, 5, 6, 4, 0, 5, 3, 0, 4, 2, 8, 8, 5, 0, 9, 1, 3, 8, 8, 5, 5, 8, 6, 1, 9, 3, 5, 2, 4, 9, 7, 6
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
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
Sequence in context: A086516 A281962 A358415 * A245617 A109205 A285294
KEYWORD
nonn,cons
AUTHOR
STATUS
approved