A245675 Decimal expansion of 'nu', a coefficient related to the variance for searching corresponding to patricia tries.

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

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

Cf. A086311, A086312.

Sequence in context: A086516 A281962 A358415 * A245617 A109205 A285294

Adjacent sequences: A245672 A245673 A245674 * A245676 A245677 A245678

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 29 2014

Status

approved