A336284 Decimal expansion of Sum_{n>=2} n^(log(n))/log(n)^n.

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

Offset: 2

Author

Bernard Schott, Jul 17 2020

Keywords

• nonn
• cons

Comments

This series is convergent because there exists n_1 such that for n >= n_1, n^(log(n))/log(n)^n <= (1/sqrt(e))^n.

Examples

			10.5417051152289715912697153360630929474717489965883...
		

Crossrefs

Cf. A073009 (1/n^n), A099870 (1/n^log(n)), A099871 (1/log(n)^n), A308915 (1/(log(n)^log(n))).

Cf. A092605 (1/sqrt(e)).

Programs

Maple

evalf(sum(n^(log(n))/log(n)^n, n=2..infinity),100);

PARI

suminf(n=2, n^(log(n))/log(n)^n) \\ Michel Marcus, Jul 17 2020

Formula

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