A174815 Decimal expansion of sqrt(2)*e^(gamma), where gamma is Euler's constant.

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

Offset

1,1

Comments

This constant appears when comparing various divergent series after n iterations.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Mersenne Prime

Wikipedia, Euler-Mascheroni constant

Formula

lim_{n->oo} e^sum(1/k, k=1..n) / sqrt(1+2+3+...+n) = sqrt(2)*e^gamma.

Example

sqrt(2)*e^(gamma) = 2.5188167690903800744959345354177803788433360213612...

Maple

evalf(sqrt(2)*exp(gamma), 99);

Mathematica

RealDigits[Sqrt[2]*Exp[EulerGamma], 10, 100][[1]] (* G. C. Greubel, Sep 06 2018 *)

Prog

(PARI) sqrt(2)*exp(Euler)  \\ Charles R Greathouse IV, Aug 01 2011
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2)* Exp(EulerGamma(R)); // G. C. Greubel, Sep 06 2018

Crossrefs

Equals A002193*A001113^A001620.

Sequence in context: A268980 A297012 A259449 * A021401 A280637 A271872

Adjacent sequences: A174812 A174813 A174814 * A174816 A174817 A174818

Keyword

nonn,cons

Author

Ryan Gerard (rsgerard(AT)gmail.com), Mar 29 2010

Extensions

Comments containing infinities removed by Jonathan Sondow, Aug 01 2011

Status

approved