A336987 Decimal expansion of Sum_{n>=2} sqrt(n)^log(n)/log(n)^sqrt(n).

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

Offset

2,1

Comments

The series u(n) = sqrt(n)^log(n)/log(n)^sqrt(n) is convergent because n^2 * u(n) -> 0 when n -> oo.

References

J. Moisan & A. Vernotte, Analyse, Topologie et Séries, Exercices corrigés de Mathématiques Spéciales, Ellipses, 1991, Exercice B-1 a-3 pp. 70, 87-88.

Links

Table of n, a(n) for n=2..101.

Formula

Equals Sum_{n>=2} sqrt(n)^log(n)/log(n)^sqrt(n).

Example

32.219419584243365152435936117722884...

Maple

evalf(sum(sqrt(n)^log(n)/log(n)^sqrt(n), n=2..infinity), 120);

Prog

(PARI) default(realprecision, 100); sumpos(n=2, sqrt(n)^log(n)/log(n)^sqrt(n)) \\ Michel Marcus, Aug 10 2020

Crossrefs

Cf. A099870, A308915, A336284, A336741.

Sequence in context: A071048 A357104 A098054 * A075801 A243160 A272694

Adjacent sequences: A336984 A336985 A336986 * A336988 A336989 A336990

Keyword

nonn,cons

Author

Bernard Schott, Aug 10 2020

Extensions

a(37)-a(101) from Robert Price, Aug 21 2020

Status

approved