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 A365066 #17 Mar 27 2025 23:27:32
%S A365066 6,3,4,5,5,1,1,1,8,2,6,1,2,2,5,5,4,2,7,5,7,6,1,4,2,4,1,3,0,9,6,0,7,7,
%T A365066 2,2,3,6,3,0,7,9,9,5,0,2,5,1,6,3,2,6,5,5,8,7,5,4,8,9,1,1,6,8,7,6,9,7,
%U A365066 3,1,4,8,0,3,1,3,9,9,5,3,5,3,8,5,6,5,6,8,3,0,6,6,4,9,6,5,1,1,6,9,8,9,8,2,7
%N A365066 Decimal expansion of the constant 1/0! - 1/1! + 1/2! + 1/3! - 1/4! + 1/5! + 1/6! - 1/7! + ...
%F A365066 Equals e - 2*A143820.
%F A365066 Equals Sum_{n>=0} (-1)^(2^((n-1) mod 3) mod 2) / n! = e/3 - 4*sin(sqrt(3)/2 - Pi/6) / (3*sqrt(e)).
%F A365066 Equals Sum_{n>=0} 1/(3*n)! - 1/(3*n+1)! + 1/(3*n+2)!. - _Michal Paulovic_, Aug 19 2023
%e A365066 0.63455111826122554275761424130960772236307995025163265587548911687697314...
%p A365066 Digits:=105: evalf(sum(1/(3*n)!-1/(3*n+1)!+1/(3*n+2)!, n=0..infinity)); # _Michal Paulovic_, Aug 20 2023
%t A365066 RealDigits[E/3 - (4*Sin[Sqrt[3]/2-Pi/6])/(3*Sqrt[E]), 10, 105][[1]]
%o A365066 (PARI) suminf(n=0,1/(3*n)!-1/(3*n+1)!+1/(3*n+2)!) \\ _Michal Paulovic_, Aug 20 2023
%Y A365066 Cf. A143820.
%K A365066 nonn,cons
%O A365066 0,1
%A A365066 _Peter McNair_, Aug 19 2023