This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113554 #21 Mar 29 2024 19:31:51 %S A113554 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 A113554 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 A113554 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 A113554 Decimal expansion of average of e^(1/e) and Pi. %C A113554 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 A113554 For the Foias constant F satisfying FRF = fRf, F*f is very close to the third zero of the Riemann zeta function. %H A113554 Danny Rorabaugh, <a href="/A113554/b113554.txt">Table of n, a(n) for n = 1..10000</a> %F A113554 Equals (Pi + e^(1/e))/2. %e A113554 2.2931302572997796860604912459379665536278824263086794933977336283... %t A113554 First[RealDigits[N[(E^(1/E) + Pi)/2, 100]]] (* _Ryan Propper_, Jul 21 2006 *) %o A113554 (SageMath) N((pi+exp(exp(-1)))/2,digits=107) # _Danny Rorabaugh_, Mar 26 2015 %o A113554 (PARI) (exp(exp(-1))+Pi)/2 \\ _Charles R Greathouse IV_, Mar 10 2016 %o A113554 (Magma) R:= RealField(100); (Pi(R) + Exp(1/Exp(1)))/2; // _G. C. Greubel_, Aug 31 2018 %K A113554 cons,nonn,easy %O A113554 1,1 %A A113554 _Marco Matosic_, Jan 13 2006 %E A113554 a(18)-a(100) from _Ryan Propper_, Jul 21 2006 %E A113554 a(99)-a(100) corrected and a(101)-a(105) added by _Danny Rorabaugh_, Mar 26 2015