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%I #21 Mar 29 2024 19:31:51
%S 2,2,9,3,1,3,0,2,5,7,2,9,9,7,7,9,6,8,6,0,6,0,4,9,1,2,4,5,9,3,7,9,6,6,
%T 5,5,3,6,2,7,8,8,2,4,2,6,3,0,8,6,7,9,4,9,3,3,9,7,7,3,3,6,2,8,3,0,5,8,
%U 3,5,6,7,2,0,0,2,4,1,1,7,5,2,1,0,0,8,0,8,8,7,4,1,9,4,6,0,7,9,5,9,5,6,2,5,5
%N Decimal expansion of average of e^(1/e) and Pi.
%C Close to A085846 which is also close to the product Zeta(2...s) and this is itself close to 2e-Pi. The e-th root of e, eRe, is the maximum for any aRa = bRb pair. See A085846. Likewise for a^b = b^a pairs there is a minimum, e^e.
%C For the Foias constant F satisfying FRF = fRf, F*f is very close to the third zero of the Riemann zeta function.
%H Danny Rorabaugh, <a href="/A113554/b113554.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals (Pi + e^(1/e))/2.
%e 2.2931302572997796860604912459379665536278824263086794933977336283...
%t First[RealDigits[N[(E^(1/E) + Pi)/2, 100]]] (* _Ryan Propper_, Jul 21 2006 *)
%o (SageMath) N((pi+exp(exp(-1)))/2,digits=107) # _Danny Rorabaugh_, Mar 26 2015
%o (PARI) (exp(exp(-1))+Pi)/2 \\ _Charles R Greathouse IV_, Mar 10 2016
%o (Magma) R:= RealField(100); (Pi(R) + Exp(1/Exp(1)))/2; // _G. C. Greubel_, Aug 31 2018
%K cons,nonn,easy
%O 1,1
%A _Marco Matosic_, Jan 13 2006
%E a(18)-a(100) from _Ryan Propper_, Jul 21 2006
%E a(99)-a(100) corrected and a(101)-a(105) added by _Danny Rorabaugh_, Mar 26 2015
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