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

%I #23 Jul 20 2020 11:52:48

%S 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,

%T 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,

%U 3,4,7,2,6,3,5,4,3,0,5,7,7,0,2,9,3,5,9,9,7

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

%C 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.

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

%e 10.5417051152289715912697153360630929474717489965883...

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

%o (PARI) suminf(n=2, n^(log(n))/log(n)^n) \\ _Michel Marcus_, Jul 17 2020

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

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

%K nonn,cons

%O 2,3

%A _Bernard Schott_, Jul 17 2020