login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164985 Denominators of ternary BBP-type series for log(5) 3
1, 6, 27, 405, 1458, 5103, 59049, 196830, 649539, 6908733, 22320522, 71744535, 731794257, 2324522934, 7360989291, 73222472421, 230127770466, 721764371007, 7060738412025, 22029503845518, 68630377364883, 663426981193869 (list; graph; refs; listen; history; text; internal format)
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: A267630 A047778 A290802 * A048436 A276412 A006174

Adjacent sequences:  A164982 A164983 A164984 * A164986 A164987 A164988

KEYWORD

frac,nonn

AUTHOR

Jaume Oliver Lafont, Sep 03 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)