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

0,2

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)

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A154920.

Sequence in context: A367886 A351735 A322233 * A367884 A048436 A276412

Adjacent sequences: A164982 A164983 A164984 * A164986 A164987 A164988

Keyword

frac,nonn

Author

Jaume Oliver Lafont, Sep 03 2009

Status

approved