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 A365307 #27 Oct 29 2023 18:18:44
%S A365307 2,2,9,0,6,1,6,6,9,2,7,8,5,3,6,2,4,2,2,1,0,7,5,3,3,4,1,4,5,6,1,8,4,5,
%T A365307 0,2,5,7,8,2,0,6,8,7,3,8,6,9,0,7,3,4,6,6,5,0,5,7,1,3,1,4,9,5,0,9,9,4,
%U A365307 1,8,8,0,3,0,4,8,7,0,1,0,8,2,5,0,1,1,9,3,9,9
%N A365307 Decimal expansion of 1/(2*e-5).
%C A365307 The continued fraction expansion is A081750 with initial term 5 omitted.
%F A365307 Equals 2 + 1/(3 + 2/(4 + 3/(5 + 4/(6 + 5/( ... /(n+1 + n/(n+2 + ... ))))))).
%F A365307 From _Peter Bala_, Oct 23 2023: (Start)
%F A365307 Define s(n) = Sum_{k = 3..n} 1/k!. Then 1/(2*e - 5) = 3 - (1/2)*Sum_{n >= 3 } 1/( (n+1)!*s(n)*s(n+1) ) is a rapidly converging series of rationals. Cf. A073333 and A194807.
%F A365307 Equivalently, 1/(2*e - 5) = 3 - (1/2)*(3!/(1*5) + 4!/(5*26) + 5!/(26*157) + 6!/(157*1100) + ...), where [1, 5, 26, 157, 1100, ... ] is A185108. (End)
%e A365307 2.2906166927853624221...
%t A365307 A365307 = RealDigits[N[1/(2*E-5),#+1]][[1]][[1;;-2]]&;
%o A365307 (PARI) 1/(2*exp(1)-5).
%Y A365307 Cf. A001113, A194807, A019762, A113011, A081750, A073333, A185108.
%K A365307 nonn,cons
%O A365307 1,1
%A A365307 _Rok Cestnik_, Aug 31 2023