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

Author

Jean-François Alcover, Jul 29 2014

Keywords

• nonn
• cons

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.

Examples

			1.000000000001237412575736110228719610646672874297732...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.11 Feller's coin tossing p. 341 and Section 5.14 Digital Search Tree Constants p. 356.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Wikipedia, Radix tree

Crossrefs

Cf. A086311, A086312.

Programs

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

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)).