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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
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
Sequence in context: A373682 A166899 A201534 * A165206 A095664 A215773
KEYWORD
frac,nonn
AUTHOR
Benoit Cloitre, Oct 19 2002
EXTENSIONS
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved