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A246499 Decimal expansion of zeta(2)/exp(gamma), gamma being the Euler-Mascheroni constant. 3
9, 2, 3, 5, 6, 3, 8, 3, 1, 6, 7, 4, 1, 8, 1, 3, 8, 2, 3, 2, 3, 5, 0, 9, 9, 5, 3, 9, 8, 7, 7, 0, 3, 9, 1, 6, 8, 4, 6, 9, 3, 1, 9, 6, 3, 2, 6, 1, 1, 1, 6, 3, 2, 5, 2, 0, 3, 5, 9, 5, 8, 3, 1, 6, 0, 2, 9, 7, 2, 3, 4, 3, 0, 5, 8, 2, 6, 0, 4, 8, 0, 9, 0, 9, 1, 2, 4, 9, 7, 7, 5, 0, 5, 2, 6, 5, 6, 2, 9, 8, 7, 9, 1, 5, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
It follows from Mertens theorem that this constant is the limit for large m of log(prime(m))*Product_{k=1..m} 1/(1 + 1/prime(k)).
LINKS
Eric Weisstein's World of Mathematics, Mertens Theorem, Equations 5-9
FORMULA
Equals Pi^2/(6*exp(gamma)).
Equals lim_{m->infinity} log(prime(m))*Product_{k=1..m} 1/(1 + 1/prime(k)).
Equals A013661/A073004. - Michel Marcus, Nov 18 2014
EXAMPLE
0.9235638316741813823235099539877039168469319632611163252035958316...
MATHEMATICA
RealDigits[Zeta[2]/E^EulerGamma, 10, 100][[1]] (* Alonso del Arte, Nov 14 2014 *)
PROG
(PARI) Pi^2/6/exp(Euler)
(Magma) R:=RealField(100); Pi(R)^2/(6*Exp(EulerGamma(R))); // G. C. Greubel, Aug 30 2018
CROSSREFS
Sequence in context: A104539 A201559 A300015 * A199002 A160108 A011344
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, Nov 14 2014
STATUS
approved

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Last modified June 12 14:38 EDT 2024. Contains 373331 sequences. (Running on oeis4.)