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.

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

Offset

0,1

Comments

Sometimes called Ioachimescu's constant, after the Romanian mathematician and engineer Andrei Gheorghe Ioachimescu (1868-1943). - Amiram Eldar, Apr 02 2022

References

Vasile Berinde and Eugen Păltănea, Gazeta Matematică - A Bridge Over Three Centuries, Romanian Mathematical Society, 2004, pp. 113-114.

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

A. G. Ioachimescu, Problem 16, Gazeta Matematică, Vol. 1, No. 2 (1895), p. 39.

Links

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

Chao-Ping Chen, Ioachimescu's constant, Research Group in Mathematical Inequalities and Applications, Vol. 13. No. 1 (2010).

Alina Sîntămărian, A Generalisation of Ioachimescu's Constant, The Mathematical Gazette, Vol. 93, No. 528 (2009), pp. 456-467.

Alina Sîntămărian, Regarding a generalisation of Ioachimescu's constant, The Mathematical Gazette, Vol. 94, No. 530 (2010), pp. 270-283.

Alina Sîntămărian, Sequences that converge quickly to a generalized Euler constant, Mathematical and Computer Modelling, Vol. 53, No. 5-6 (2011), pp. 624-630.

Xu You, Di-Rong Chen, and Hong Shi, Some new sequences that converge to the Ioachimescu constant, Journal of Inequalities and Applications, Vol. 2016, No. 1 (2016), Article 148.

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-François Alcover, May 19 2014

Status

approved