A137987 Decimal expansion of the inverse of the number whose Engel expansion has the sequence of factorial numbers (A000142) as coefficients.

3, 8, 6, 5, 7, 2, 8, 5, 1, 1, 2, 0, 0, 8, 5, 1, 2, 8, 5, 3, 8, 8, 3, 3, 5, 3, 0, 4, 8, 7, 3, 9, 2, 3, 2, 6, 8, 0, 1, 1, 2, 7, 2, 9, 8, 5, 8, 9, 2, 7, 4, 6, 4, 6, 8, 8, 9, 2, 5, 2, 2, 1, 3, 4, 4, 0, 4, 1, 0, 1, 1, 7, 3, 4, 1, 4, 5, 8, 4, 0, 7, 3, 3, 2, 1, 0, 1, 3, 6, 7, 0, 3, 3, 5, 9, 3, 9, 4, 7

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Feb 26 2008, Apr 18 2008

Keywords

• easy
• nonn
• cons

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Eric Weisstein's World of Mathematics, Pierce Expansion.
• Eric Weisstein's World of Mathematics, Engel Expansion.

Crossrefs

Cf. A000142, A137986, A137988, A137989, A287013.

Programs

Maple

P:=proc(n) local a,i,k; a:=0; k:=1; for i from 0 by 1 to n do k:=k*i!; a:=a+1/k; print(evalf(1/a,100)); od; end: P(100);

Mathematica

RealDigits[N[(1/Sum[Product[1/((k - 1)!), {k, 1, n}], {n, 1, 250}]), 100]][[1]] (* G. C. Greubel, Jan 02 2017 *)

Formula

Equals 1/A287013. - Amiram Eldar, Nov 19 2020