A108745 Decimal expansion of C = 1/(1+2/(1+3/(1+5/(1+6/(1+8/(1+9/(1+11/(1+. .)))))))).

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

Offset: 0

Author

Philippe Deléham, Jun 22 2005

Keywords

• nonn
• cons

Examples

			0.50782973248...
		

Crossrefs

Cf. A108743, A108744.

Programs

Mathematica

E^(1/3)*ExpIntegralE[2/3, 1/3]/3 // RealDigits[#, 10, 104]& // First (* Jean-François Alcover, Feb 22 2013 *)

PARI

{C=1;oo=10^5;sum(k=1,oo,C=1./(1+(3*(oo-k+1)-1)/(1+3*(oo-k+1)*C)));return(C)} /* Paul D. Hanna */

Formula

A = B + C with A = Gamma(1/3)*(e/9)^(1/3) and B = Sum_{ = n > 0 } 1/A007559(n).

C = Gamma(1/3, 1/3)*(e/9)^(1/3). - Vladeta Jovovic, Jun 26 2005

Extensions

More terms from Paul D. Hanna, Jun 25 2005