A244257 Decimal expansion of the asymptotic evaluation of the constrained maximum of a certain quadratic form.

2, 3, 9, 7, 9, 4, 5, 5, 8, 6, 1, 1, 4, 4, 3, 6, 3, 3, 7, 4, 0, 6, 1, 3, 9, 3, 7, 8, 9, 0, 6, 0, 6, 6, 0, 5, 5, 8, 8, 0, 8, 2, 3, 4, 0, 0, 1, 5, 7, 6, 3, 1, 1, 6, 0, 3, 1, 1, 1, 4, 9, 9, 7, 9, 3, 5, 1, 9, 1, 3, 6, 8, 6, 7, 9, 7, 6, 4, 5, 1, 9, 8, 5, 5, 7, 4, 8, 7, 9, 1, 1, 9, 5, 9, 4, 3, 3, 3, 7, 7

Offset

1,1

Comments

The quadratic form to maximize is (sum_(k>=1) x(k)/k)^2 + sum_(k>=1) (x(k)/k)^2, subject to the constraint (sum_(k>=1) x(k)^2) <= 1.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.12 Du Bois Reymond's constants, p. 239.

Links

Table of n, a(n) for n=1..100.

Formula

(Pi/xi)^2, where xi is the smallest positive solution of the equation x+tan(x)=0.

Example

2.397945586114436337406139378906...

Mathematica

xi = x /. FindRoot[x + Tan[x] == 0, {x, 2}, WorkingPrecision -> 100]; RealDigits[(Pi/xi)^2] // First

Crossrefs

Cf. A196504.

Sequence in context: A340442 A199963 A016634 * A171054 A205860 A318948

Adjacent sequences: A244254 A244255 A244256 * A244258 A244259 A244260

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 24 2014

Status

approved