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%I #5 Jun 30 2021 02:39:23
%S 2,4,3,2,3,8,3,4,2,8,9,0,9,8,0,7,5,5,4,1,5,0,5,9,1,3,5,4,6,5,4,6,2,3,
%T 0,7,1,7,8,3,0,4,9
%N Decimal expansion of Integral_{x>=0} (zeta(x)-1) dx (negated).
%C Robinson (1980) conjectured and Newman and Widder (1981) proved that this integral is equal to the limit given in the Formula section.
%D Murray S. Klamkin (ed.), Problems in Applied Mathematics: Selections from SIAM Review, Philadelphia, PA: Society for Industrial and Applied Mathematics, 1990, pp. 281-282.
%H H. P. Robinson, <a href="http://www.jstor.org/stable/2029968">A Conjectured Limit</a>, Problem 80-7, SIAM Review, Vol. 22, No. 2 (1980), p. 229; D. J. Newman and D. V. Widder, <a href="http://www.jstor.org/stable/2030000">Solution</a>, ibid., Vol. 23, No. 2 (1981), pp. 256-257.
%F Equals lim_{n->oo} (Sum_{k=2..n} 1/log(k) - Integral_{x=0..n} (1/log(x)) dx).
%e -0.2432383428909807554150591354654623071783049...
%Y Cf. A099769, A168218.
%K nonn,cons,more
%O 0,1
%A _Amiram Eldar_, Jun 29 2021