%I #34 Oct 21 2021 16:36:43
%S 6,7,1,6,9,7,0,6,1,2,9,9,0,8,9,6,0,8,8,1,4,4,5,7,9,9,8,7,2,3,2,6,0,8,
%T 8,9,1,4,5,2,7,7,2,6,1,6,5,8,8,4,5,0,4,5,8,2,6,7,0,7,5,9,2,8,4,0,5,2,
%U 4,0,2,1,8,0,6,9,3,2,5,0,9,4,3,3,5,1,1,0,0,1,8,7,5,7,2,7,6,4,2
%N Decimal expansion of Sum_{n>=1} 1/(log(n)^log(n)).
%C This series is convergent because n^2 * 1/log(n)^log(n) = exp(log(n) * (2 - log(log(n)))) which -> 0 as n -> oo.
%D Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.2.1.i p. 279.
%F Equals Sum_{n>=1} 1/(log(n)^log(n)).
%e 6.71697061299089608814457...
%p evalf(sum(1/(log(n)^log(n)), n=1..infinity), 110);
%t RealDigits[N[1 + Sum[1/Log[n]^Log[n], {n, 2, Infinity}], 100]][[1]] (* _Jinyuan Wang_, Jul 25 2019 *)
%o (PARI) 1 + sumpos(n=2, 1/(log(n)^log(n))) \\ _Michel Marcus_, Jun 30 2019
%Y Cf. A073009 (1/n^n), A099870 (1/n^log(n)), A099871 (1/log(n)^n).
%K cons,nonn
%O 1,1
%A _Bernard Schott_, Jun 30 2019
%E More terms from _Jon E. Schoenfield_, Jun 30 2019
%E a(16)-a(24) from _Jinyuan Wang_, Jul 10 2019
%E More terms from _Charles R Greathouse IV_, Oct 21 2021