login
Decimal expansion of Sum_{n = 1, ..., infinity } 1/n^(2^n).
1

%I #15 Sep 29 2023 19:47:48

%S 1,0,6,2,6,5,2,4,1,6,0,2,3,1,0,6,5,1,6,2,3,4,3,1,1,9,0,7,9,4,9,7,3,2,

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

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

%N Decimal expansion of Sum_{n = 1, ..., infinity } 1/n^(2^n).

%C The sum converges very quickly and therefore just a few summands are quite enough to get the value accurate to hundreds of decimal places. For example, 1/10^(2^10) = 10^(-1024), meaning that the impact of n = 10 on the sum can't be seen among the first thousand decimal digits. - _Alonso del Arte_, Sep 21 2012

%e 1.0626524160231065162343119079497327861...

%p evalf(sum(1/n^(2^n), n=1..infinity), 140); # _Alois P. Heinz_, Sep 29 2023

%t RealDigits[Sum[1/n^(2^n), {n, 10}], 10, 105][[1]] (* _T. D. Noe_, Sep 21 2012 *)

%o (PARI) suminf(n=1,1/n^2^n) \\ _Charles R Greathouse IV_, Apr 21 2016

%Y Cf. A097547.

%K cons,easy,nonn

%O 1,3

%A _Nicolas M. Perrault_, Sep 21 2012