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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. 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, 2, 6, 8, 4, 5, 3, 3, 4, 0 (list; constant; graph; refs; listen; history; text; internal format)
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: A086516 A281962 A245675 * A109205 A285294 A115630

Adjacent sequences:  A245614 A245615 A245616 * A245618 A245619 A245620

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Nov 05 2014

STATUS

approved

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Last modified January 20 10:55 EST 2022. Contains 350472 sequences. (Running on oeis4.)