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%I A003521 M4418 #30 Feb 03 2020 10:26:22
%S A003521 1,7,37,58,163,4687,30178,30493,47338,83218,106177,134773,288502,
%T A003521 991027
%N A003521 Values of m in the discriminant D = -4*m leading to a new minimum of the L-function of the Dirichlet series L(1) = Sum_{k>=1} Kronecker(D,k)/k.
%C A003521 In Shanks's Table 3 "Lochamps, -4N = Discriminant", N = 1 is omitted. Shanks describes the table as being tentative after N = 47338. In Buell's Table 7 "Successive minima of L(1) for even discriminants" several omissions and extra terms are present for N < 30178, but the terms above are confirmed by an independent computation. - _Hugo Pfoertner_, Feb 03 2020
%D A003521 D. Shanks, Systematic examination of Littlewood's bounds on L(1,chi), pp. 267-283 of Analytic Number Theory, ed. H. G. Diamond, Proc. Sympos. Pure Math., 24 (1973). Amer. Math. Soc.
%D A003521 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003521 Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796 (Table 7, page 791).
%H A003521 D. Shanks, <a href="/A003419/a003419.pdf">Systematic examination of Littlewood's bounds on L(1,chi)</a>, Proc. Sympos. Pure Math., 24 (1973). Amer. Math. Soc. (Annotated scanned copy)
%e A003521 With L1(k) = L(1) for D=-4*k:
%e A003521 a(1) = 1: L1(1) ~= 0.785398... = Pi/4;
%e A003521 L1(2) = 1.1107, L1(3) = 0.9069, L1(4) = 0.7854, L1(5) = 1.4050, L1(6) = 1.2825, all >= a(1);
%e A003521 a(2) = 7 because L1(7) = 0.5937 < a(1);
%e A003521 a(3) = 37 because L1(k) > a(2) for 8 <= k <= 36, L1(37) = 0.51647 < a(2).
%Y A003521 Cf. A003420.
%K A003521 nonn,more
%O A003521 1,2
%A A003521 _N. J. A. Sloane_
%E A003521 New title, a(1) prepended and a(10)-a(14) from _Hugo Pfoertner_, Feb 03 2020

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