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%I A003420 M1387 #35 Aug 27 2022 21:31:23
%S A003420 1,2,5,11,14,26,41,89,101,194,314,341,689,1091,1154,1889,2141,3449,
%T A003420 3506,5561,6254,8126,8774,10709,13166,15461,23201,24569,30014,81149,
%U A003420 81626,162686,243374,644474,839354,879941
%N A003420 Values of m in the discriminant D = -4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k=1..oo} Kronecker(D,k)/k.
%C A003420 In Shanks's Table 5 "Hichamps, -4N = Discriminant", N = 1 is omitted, and N = 23201 is missing. Shanks describes the table as being tentative after N = 24569. In Buell's Table 10 "Successive maxima of L(1) for even discriminants", the values N = 11 and N = 1091 are missing in the D/4 column. The further terms 644474, 839354, 879941, provided there require an independent check. - _Hugo Pfoertner_, Feb 02 2020
%D A003420 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 A003420 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003420 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 10, page 792).
%H A003420 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 A003420 a(1) = 1: L(1) for D=-4*1 ~= 0.785398... = Pi/4.
%e A003420 a(2) = 2: L(1) for D=-4*2 ~= 1.11072073... = Pi/(2*sqrt(2)), a(2) > a(1);
%e A003420 L(1) for D=-4*3 ~= 0.90689..., L(1) for D=-4*4 ~= 0.785398..., both < a(2);
%e A003420 a(3) = 5: L(1) for D=-4*5 = 1.40496..., a(3) > a(2).
%Y A003420 Cf. A003521.
%Y A003420 Cf. A331949, which has almost identical terms.
%K A003420 nonn,more
%O A003420 1,2
%A A003420 _N. J. A. Sloane_
%E A003420 New title, a(1) prepended, missing term 23201 and a(29)-a(33) from _Hugo Pfoertner_, Feb 02 2020
%E A003420 3 further terms < 10^6 added by _Hugo Pfoertner_, Aug 27 2022

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