A059457 Numerator of Sum_{k=0..n} (-1)^k/(3*k+1).

1, 3, 25, 111, 1583, 5877, 118943, 1239213, 6500369, 6228669, 200696339, 3293919963, 125884243831, 122175729021, 5401896940303, 121054306890369, 868338554787383, 848589287072283, 867261322002923, 24637097377492167

Offset: 0

Author

Benoit Cloitre, Oct 19 2002

Keywords

• frac
• nonn

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

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Programs

Mathematica

Table[Numerator[Sum[(-1)^k/(3*k + 1), {k, 0, n}]], {n, 0, 50}] (* G. C. Greubel, Oct 04 2017 *)

PARI

a(n)=numerator(sum(k=0,n,(-1)^k/(3*k+1)))

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

Extensions

Corrected by T. D. Noe, Oct 25 2006