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A113276 Decimal expansion of de Bruijn's constant. 0
1, 1, 0, 6, 4, 9, 5, 7, 7, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

From Amiram Eldar, Jun 22 2021: (Start)

The minimal number c such that for any sequence of nonnegative numbers b(k) the following inequality always holds: Sum_{k>=1} b(k) <= c * Sum_{k>=1} sqrt(Sum_{i>=k} b(i)^2/k).

Also called the Copson-de Bruijn constant after the British mathematician Edward Thomas Copson (1901-1980) and the Dutch mathematician Nicolaas Govert de Bruijn (1918-2012). (End)

REFERENCES

R. P. Boas and N. G. de Bruijn, Solution for problem 83, Wiskundige Opgaven met de Oplossingen, Vol. 20 (1957), pp. 2-4.

N. G. de Bruijn, Asymptotic Methods in Analysis, New York: Dover, 1981. See p. 174.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 217-219.

LINKS

Table of n, a(n) for n=1..11.

E. T. Copson, Note on Series of Positive Terms, J. London Math. Soc., Vol. 2 (1927), pp. 9-12.

E. T. Copson, Note on Series of Positive Terms, J. London Math. Soc., Vol. 3 (1928), pp. 49-51.

Eric Weisstein's World of Mathematics, de Bruijn Constant.

EXAMPLE

1.1064957714...

CROSSREFS

Sequence in context: A333322 A348896 A153630 * A086034 A191622 A021943

Adjacent sequences:  A113273 A113274 A113275 * A113277 A113278 A113279

KEYWORD

nonn,cons,hard,more

AUTHOR

Eric W. Weisstein, Oct 21 2005

STATUS

approved

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Last modified September 26 17:47 EDT 2022. Contains 357002 sequences. (Running on oeis4.)