A099871 - OEIS

%I #13 Feb 06 2024 14:18:10

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

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

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

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

%H G. C. Greubel, <a href="/A099871/b099871.txt">Table of n, a(n) for n = 1..1000</a>

%e 3.2426094109252482106020387...

%p evalf(sum(1/(log(n)^n),n=2..5000),105);

%t digits = 105; NSum[1/Log[n]^n, {n, 2, Infinity}, NSumTerms -> 2*digits, WorkingPrecision -> digits+1] // RealDigits[#, 10, digits] & // First (* _Jean-François Alcover_, Feb 21 2014 *)

%o (PARI) default(realprecision, 100); sum(k=2, 1000, 1/log(k)^k) \\ _G. C. Greubel_, Nov 20 2018

%o (Magma) SetDefaultRealField(RealField(100)); [(&+[1/Log(k)^k: k in [2..1000]])]; // _G. C. Greubel_, Nov 20 2018

%o (Sage) numerical_approx(sum(1/log(k)^k for k in [2..1000]), digits=100) # _G. C. Greubel_, Nov 20 2018

%K cons,easy,nonn

%O 1,1

%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 02 2004

%E Edited by _N. J. A. Sloane_, May 16 2008 at the suggestion of _R. J. Mathar_