A164985 Denominators of ternary BBP-type series for log(5).

1, 6, 27, 405, 1458, 5103, 59049, 196830, 649539, 6908733, 22320522, 71744535, 731794257, 2324522934, 7360989291, 73222472421, 230127770466, 721764371007, 7060738412025, 22029503845518, 68630377364883, 663426981193869

Offset: 0

Author

Jaume Oliver Lafont, Sep 03 2009

Keywords

• frac
• nonn

Comments

The formula

log(5)=(4/27)Sum(k>=0,(1/81^k)(9/(4k+1)+3/(4k+2)+1/(4k+3)))

can be written in unit numerators:

log(5)=(4/3)Sum(k>=0,(1/81^k)(1/(4k+1)+1/(3*(4k+2))+1/(9*(4k+3)))),

so the sequence of denominators inside the sum satisfies

Sum(n>=0,1/a(n))=(3/4)log(5)

Crossrefs

Cf. A154920.

Programs

PARI

a(n)=[(n\3*4+1),3*(n\3*4+2),9*(n\3*4+3)][n%3+1]*81^(n\3)

Formula

G.f.: (1+6*x+27*x^2+243*x^3+486*x^4+729*x^5)/(1-81*x^3)^2