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%I #17 Dec 25 2023 17:35:03
%S 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,
%T 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,
%U 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
%N 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.
%C Sometimes called Ioachimescu's constant, after the Romanian mathematician and engineer Andrei Gheorghe Ioachimescu (1868-1943). - _Amiram Eldar_, Apr 02 2022
%D Vasile Berinde and Eugen Păltănea, Gazeta Matematică - A Bridge Over Three Centuries, Romanian Mathematical Society, 2004, pp. 113-114.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.5.3, p. 32.
%D A. G. Ioachimescu, Problem 16, Gazeta Matematică, Vol. 1, No. 2 (1895), p. 39.
%H G. C. Greubel, <a href="/A242616/b242616.txt">Table of n, a(n) for n = 0..10000</a>
%H Chao-Ping Chen, <a href="https://rgmia.org/papers/v13n1/chen.pdf">Ioachimescu's constant</a>, Research Group in Mathematical Inequalities and Applications, Vol. 13. No. 1 (2010).
%H Alina Sîntămărian, <a href="https://www.jstor.org/stable/40378562">A Generalisation of Ioachimescu's Constant</a>, The Mathematical Gazette, Vol. 93, No. 528 (2009), pp. 456-467.
%H Alina Sîntămărian, <a href="https://www.jstor.org/stable/25759666">Regarding a generalisation of Ioachimescu's constant</a>, The Mathematical Gazette, Vol. 94, No. 530 (2010), pp. 270-283.
%H Alina Sîntămărian, <a href="https://doi.org/10.1016/j.mcm.2010.09.014">Sequences that converge quickly to a generalized Euler constant</a>, Mathematical and Computer Modelling, Vol. 53, No. 5-6 (2011), pp. 624-630.
%H Xu You, Di-Rong Chen, and Hong Shi, <a href="https://doi.org/10.1186/s13660-016-1089-x">Some new sequences that converge to the Ioachimescu constant</a>, Journal of Inequalities and Applications, Vol. 2016, No. 1 (2016), Article 148.
%F Equals zeta(1/2) + 2.
%e 0.53964549119041318711050084748470198753277...
%t RealDigits[Zeta[1/2] + 2, 10, 100] // First
%o (PARI) default(realprecision, 100); zeta(1/2)+2 \\ _G. C. Greubel_, Sep 04 2018
%o (Magma) SetDefaultRealField(RealField(100)); L:=RiemannZeta(); 2 + Evaluate(L, 1/2) // _G. C. Greubel_, Sep 04 2018
%Y Cf. A001620, A059750, A082633.
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, May 19 2014
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