A086312 -id:A086312 - cp's OEIS frontend

A086311 Decimal expansion of constant appearing in the variance for searching in a digital tree.

2, 8, 4, 4, 3, 8, 3, 1, 6, 8, 1, 1, 6, 7, 5, 6, 1, 6, 8, 2, 1, 6, 2, 2, 5, 7, 2, 3, 1, 4, 1, 0, 0, 8, 2, 6, 6, 4, 8, 9, 0, 3, 8, 5, 3, 0, 9, 0, 8, 7, 1, 0, 7, 7, 4, 3, 9, 5, 5, 3, 7, 5, 4, 6, 6, 6, 3, 6, 8, 1, 9, 0, 2, 3, 9, 4, 2, 4, 1, 2, 7, 7, 7, 4, 8, 8, 2, 1, 9, 5, 7, 9, 1, 7, 1, 8, 4, 8, 8, 0, 2, 5

Offset: 1

Eric W. Weisstein, Jul 15 2003

			2.84438316811675616821622572314100826648903853090871...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 356.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Tree Searching

Cf. A086312.

digits = 102; alpha =  NSum[1/(2^k-1), {k, 1, 500}, NSumTerms -> 100, WorkingPrecision -> digits+10]; beta = NSum[1/(2^k-1)^2, {k, 1, 500}, NSumTerms -> 100, WorkingPrecision -> digits+10]; RealDigits[1/12 + (Pi^2+6)/(6*Log[2]^2) - alpha - beta, 10, digits] // First

1/12 + (Pi^2+6)/(6*log(2)^2) - alpha - beta, where gamma is Euler's constant, alpha is the Erdős-Borwein constant (A065442) and beta is A065443. - Jean-François Alcover, Jul 29 2014, after Steven Finch

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

Original entry on oeis.org

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

Jean-François Alcover, Jul 29 2014

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.

			1.000000000001237412575736110228719610646672874297732...

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.

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

Cf. A086311, A086312.

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

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)).

cp's OEIS Frontend

A086311 Decimal expansion of constant appearing in the variance for searching in a digital tree.

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