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A294514
Decimal expansion of (3/2)*log(3) - Pi/(2*sqrt(3)).
1
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).
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
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