A245617 Decimal expansion of 'chi', a constant appearing in the asymptotic variance of the number of comparisons required for updating a digital search tree, in case of the "approximate counting" algorithm.

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, 2, 6, 8, 4, 5, 3, 3, 4, 0

Offset

-11,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 359.

Links

Table of n, a(n) for n=-11..88.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 44.

Eric Weisstein's Mathworld, Erdős-Borwein Constant, Tree Searching

Formula

chi = (1/log(2))*sum_{n >= 1} (1/n)*csch(2*Pi^2*(n/log(2))) = A245675 - 1.

variance ~ 1/12 + Pi^2/(6log(2)^2) - alpha - beta - chi + tau(n), where alpha is A065442, beta is A065443 and tau(n) an oscillatory negligible function.

Example

0.000000000001237412575736110228719610646672874297732...

Maple

evalf(1/log(2)*sum(1/n*csch(2*Pi^2*n/log(2)), n=1..infinity), 120) # Vaclav Kotesovec, Nov 05 2014

Mathematica

digits = 100; chi = (1/Log[2])*NSum[(1/n)*Csch[2*Pi^2*(n/Log[2])], {n, 1, Infinity}, WorkingPrecision -> digits+5]; RealDigits[chi, 10, digits] // First

Crossrefs

Cf. A065442, A065443, A245675.

Sequence in context: A281962 A358415 A245675 * A109205 A285294 A371258

Adjacent sequences: A245614 A245615 A245616 * A245618 A245619 A245620

Keyword

nonn,cons

Author

Jean-François Alcover, Nov 05 2014

Status

approved