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Decimal expansion of Sum_{n>=1} 1/n^(n^prime(n)).
0

%I #21 Nov 25 2020 21:00:53

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

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1

%N Decimal expansion of Sum_{n>=1} 1/n^(n^prime(n)).

%C Is this a finite sequence? (or equivalently, is this constant rational?)

%C Unlikely: the "apparent" rationality seems to be caused by the rapid growth of the denominators; one may instead speculate that the value is transcendental. - _Joerg Arndt_, Feb 05 2013

%C The constant is approximately 257/256 (see A021260).

%e 1.00390625000000000000000000... = 1 + 1/2^8 + 1/3^243 + 1/4^16384+...

%o (PARI) suminf(n=1,1/n^(n^prime(n)))

%Y Cf. A062481.

%K cons,nonn

%O 1,4

%A _Balarka Sen_, Aug 18 2012