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A244257 Decimal expansion of the asymptotic evaluation of the constrained maximum of a certain quadratic form. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A199858 A199963 A016634 * A171054 A205860 A318948

Adjacent sequences:  A244254 A244255 A244256 * A244258 A244259 A244260

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jun 24 2014

STATUS

approved

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Last modified August 3 04:30 EDT 2020. Contains 336197 sequences. (Running on oeis4.)