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A242616 Decimal expansion of lim_(n->infinity) ((Sum_(k=1..n) 1/sqrt(k)) - Integral_{x=1..n} 1/sqrt(x))), a generalized Euler constant which evaluates to zeta(1/2) + 2. 2
5, 3, 9, 6, 4, 5, 4, 9, 1, 1, 9, 0, 4, 1, 3, 1, 8, 7, 1, 1, 0, 5, 0, 0, 8, 4, 7, 4, 8, 4, 7, 0, 1, 9, 8, 7, 5, 3, 2, 7, 7, 0, 6, 6, 8, 9, 8, 7, 4, 1, 8, 5, 0, 9, 4, 5, 7, 1, 1, 3, 9, 1, 2, 1, 7, 4, 4, 6, 9, 4, 7, 0, 5, 2, 5, 4, 9, 9, 3, 7, 4, 7, 2, 3, 5, 8, 0, 6, 2, 4, 5, 3, 6, 6, 4, 3, 1, 8, 0, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.5.3 p. 32.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

FORMULA

Equals zeta(1/2) + 2.

EXAMPLE

0.53964549119041318711050084748470198753277...

MATHEMATICA

RealDigits[Zeta[1/2] + 2, 10, 100] // First

PROG

(PARI) default(realprecision, 100); zeta(1/2)+2 \\ G. C. Greubel, Sep 04 2018

(MAGMA) SetDefaultRealField(RealField(100)); L:=RiemannZeta(); 2 + Evaluate(L, 1/2) // G. C. Greubel, Sep 04 2018

CROSSREFS

Cf. A001620, A059750, A082633.

Sequence in context: A145800 A161501 A118273 * A073891 A196396 A086970

Adjacent sequences:  A242613 A242614 A242615 * A242617 A242618 A242619

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 19 2014

STATUS

approved

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Last modified January 29 07:03 EST 2020. Contains 331337 sequences. (Running on oeis4.)