A294514 Decimal expansion of (3/2)*log(3) - Pi/(2*sqrt(3)).

7, 4, 1, 0, 1, 8, 7, 5, 0, 8, 8, 5, 0, 5, 5, 6, 1, 1, 7, 9, 5, 8, 2, 8, 7, 2, 6, 5, 6, 2, 7, 1, 0, 6, 9, 0, 8, 2, 9, 2, 0, 2, 7, 1, 2, 6, 8, 7, 7, 5, 3, 8, 8, 9, 8, 1, 7, 0, 9, 9, 0, 3, 2, 7, 6, 2, 1, 7, 9, 8, 4, 9, 2, 6, 4, 7, 3, 6, 5, 0, 8, 4, 6, 8, 3, 6, 1, 1, 3, 8, 1, 1, 4, 5, 6, 8, 0, 4, 8, 7, 5, 3, 8, 4, 3, 8

Offset

0,1

Comments

This is the limit of the series V(3,2) := Sum_{k>=0} 1/((k + 1)*(3*k + 1)) = Sum_{k>=0} 1/A049450(k+1) = (1/2)*Sum_{k>=0} (3/(3*k + 1) - 1/(k+1)) with partial sums given in A250328(n+1)/A294513(n).

References

Max Koecher, Klassische elementare Analysis, Birkhäuser, Basel, Boston, 1987, pp. 189 - 193, with v_2(3) = (1/3)*V(3,2).

Links

Table of n, a(n) for n=0..105.

Formula

Equals V(3,2) = Sum_{k>=0} 1/((k + 1)*(3*k + 1)).

Equals Sum_{k>=2} zeta(k)/3^(k-1). - Amiram Eldar, May 31 2021

Example

0.7410187508850556117958287265627106908292027126877538898170990327...

Mathematica

RealDigits[N[(3/2)*Log[3] - Pi/(2*Sqrt[3]), 157]][[1]] (* Georg Fischer, Apr 04 2020 *)

Prog

(PARI) (3/2)*log(3) - Pi/(2*sqrt(3)) \\ Michel Marcus, Nov 02 2017

Crossrefs

Cf. A049450, A250328/A294513.

Sequence in context: A258500 A243308 A293609 * A099935 A082665 A011101

Adjacent sequences: A294511 A294512 A294513 * A294515 A294516 A294517

Keyword

nonn,cons

Author

Wolfdieter Lang, Nov 02 2017

Extensions

a(100) ff. corrected by Georg Fischer, Apr 04 2020

Data truncated by Sean A. Irvine, Apr 10 2020

Status

approved