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A086312
Decimal expansion of constant appearing in the variance for inserting in a digital tree.
3
7, 6, 3, 0, 1, 4, 1, 8, 7, 1, 1, 1, 1, 4, 8, 3, 7, 0, 3, 4, 6, 6, 4, 4, 1, 1, 9, 4, 0, 6, 0, 1, 6, 8, 4, 1, 4, 2, 4, 9, 9, 1, 3, 7, 5, 2, 6, 2, 6, 2, 9, 7, 4, 2, 7, 6, 8, 9, 7, 9, 1, 0, 9, 0, 1, 7, 5, 7, 3, 2, 1, 9, 9, 9, 3, 1, 7, 7, 2, 1, 0, 0, 0, 7, 6, 2, 0, 2, 0, 8, 1, 1, 1, 2, 8, 7, 2, 3, 4, 5, 8, 3
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 356.
LINKS
Eric Weisstein's World of Mathematics, Tree Searching
FORMULA
1/12 + Pi^2/(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
EXAMPLE
0.76301418711114837034664411940601684142499137526...
MATHEMATICA
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*Log[2]^2) - alpha - beta, 10, digits] // First
CROSSREFS
Cf. A086311.
Sequence in context: A181152 A244920 A073011 * A370746 A214280 A291081
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 15 2003
STATUS
approved