|
|
A154920
|
|
Denominators of a ternary BBP-type formula for log(3).
|
|
7
|
|
|
1, 18, 27, 324, 405, 4374, 5103, 52488, 59049, 590490, 649539, 6377292, 6908733, 66961566, 71744535, 688747536, 731794257, 6973568802, 7360989291, 69735688020, 73222472421, 690383311398, 721764371007, 6778308875544
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
log(3) = Sum_{k>=0} (9/(2k+1)+1/(2k+2))/9^(k+1).
log(3) = 1 + Sum_{k>=0} (1/(2k+2)+1/(2k+3))/9^(k+1).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n+1)*9^[(n+1)/2] = 18*a(n-2) - 81*a(n-4).
Sum_{n>=0} 1/a(n) = log(3).
Sum_{n>=0} (-1)^n/a(n) = log(8/3). - Amiram Eldar, Feb 26 2022
|
|
MATHEMATICA
|
LinearRecurrence[{0, 18, 0, -81}, {1, 18, 27, 324}, 30] (* Harvey P. Dale, Jan 10 2017 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|