A108744 Decimal expansion of B = Sum_{k>0} 1/A007559(k).

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

Offset

1,2

Links

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Formula

A = B + C with A = Gamma(1/3)*(e/9)^(1/3) and C = 1/(1+2/(1+3/(1+5/(1+6/(1+8/(1+9/(1+11/(1+. .)))))))).

Equals A108743 - A108745.

Example

1.28957855637...
Equals 1 + 1/(1*4) + 1/(1*4*7) + ...

Mathematica

E^(1/3)*(Gamma[1/3] - Gamma[1/3, 1/3])/3^(2/3) // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 22 2013 *)

Prog

(PARI) suminf(n=1, 1./prod(k=0, n-1, 3*k+1)) /* Paul D. Hanna */
(PARI) suminf(k=1, gamma(1/3)/(3^k*gamma(1/3 + k))) /* Kelvin Voskuijl, Sep 14 2025 */

Crossrefs

Cf. A007559, A016777, A108743, A108745.

Sequence in context: A340536 A388191 A340778 * A388516 A388346 A195724

Adjacent sequences: A108741 A108742 A108743 * A108745 A108746 A108747

Keyword

nonn,cons

Author

Philippe Deléham, Jun 22 2005

Extensions

More terms from Paul D. Hanna, Jun 25 2005

Status

approved