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A246499 Decimal expansion of zeta(2)/exp(gamma), gamma being the Euler-Mascheroni constant. 2
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))*prod(k=1..m, 1/(1 + 1/prime(k)) ).

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..2000

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))*prod(k=1..m, 1/(1+1/prime(k)))).

Equals lim(m->infinity)(log(prime(m))*prod(k=1..m, (1-1/prime(k)^2))/(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

Cf. A001113, A000796, A001620, A013661, A073004, A080130, A097663.

Sequence in context: A104539 A201559 A300015 * A199002 A160108 A011344

Adjacent sequences:  A246496 A246497 A246498 * A246500 A246501 A246502

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Nov 14 2014

STATUS

approved

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Last modified December 13 22:07 EST 2018. Contains 318087 sequences. (Running on oeis4.)