A086312 Decimal expansion of constant appearing in the variance for inserting in a digital tree.

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A086309 A086310 A086311 * A086313 A086314 A086315

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 15 2003

Status

approved