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

Author

Eric W. Weisstein, Jul 15 2003

Keywords

• nonn
• cons

Examples

			0.76301418711114837034664411940601684142499137526...
		

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

Crossrefs

Cf. A086311.

Programs

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

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