|
|
A059457
|
|
Numerator of Sum_{k=0..n} (-1)^k/(3*k+1).
|
|
2
|
|
|
1, 3, 25, 111, 1583, 5877, 118943, 1239213, 6500369, 6228669, 200696339, 3293919963, 125884243831, 122175729021, 5401896940303, 121054306890369, 868338554787383, 848589287072283, 867261322002923, 24637097377492167
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The denominators of Sum_{k = 0..n} (-1)^k/(3*k+1) agree with A051536 up to n = 44 but differ at n = 45. - Peter Bala, Feb 18 2024
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k>=0} (-1)^k/(3*k+1) = (log(2)*sqrt(3) + Pi)/(3*sqrt(3)).
a(n) = the numerator of the continued fraction 1/(1 + 1^2/(3 + 4^2/(3 + ... + (3*n-2)^2/(3)))). - Peter Bala, Feb 18 2024
|
|
MATHEMATICA
|
Table[Numerator[Sum[(-1)^k/(3*k + 1), {k, 0, n}]], {n, 0, 50}] (* G. C. Greubel, Oct 04 2017 *)
|
|
PROG
|
(PARI) a(n)=numerator(sum(k=0, n, (-1)^k/(3*k+1)))
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|