cp's OEIS Frontend

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.

A365066 Decimal expansion of the constant 1/0! - 1/1! + 1/2! + 1/3! - 1/4! + 1/5! + 1/6! - 1/7! + ...

Original entry on oeis.org

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, 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, 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
Offset: 0

Views

Author

Peter McNair, Aug 19 2023

Keywords

Examples

			0.63455111826122554275761424130960772236307995025163265587548911687697314...
		

Crossrefs

Cf. A143820.

Programs

  • Maple
    Digits:=105: evalf(sum(1/(3*n)!-1/(3*n+1)!+1/(3*n+2)!, n=0..infinity)); # Michal Paulovic, Aug 20 2023
  • Mathematica
    RealDigits[E/3 - (4*Sin[Sqrt[3]/2-Pi/6])/(3*Sqrt[E]), 10, 105][[1]]
  • PARI
    suminf(n=0,1/(3*n)!-1/(3*n+1)!+1/(3*n+2)!) \\ Michal Paulovic, Aug 20 2023

Formula

Equals e - 2*A143820.
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)).
Equals Sum_{n>=0} 1/(3*n)! - 1/(3*n+1)! + 1/(3*n+2)!. - Michal Paulovic, Aug 19 2023