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A003420
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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.
(Formerly M1387)
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4
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1, 2, 5, 11, 14, 26, 41, 89, 101, 194, 314, 341, 689, 1091, 1154, 1889, 2141, 3449, 3506, 5561, 6254, 8126, 8774, 10709, 13166, 15461, 23201, 24569, 30014, 81149, 81626, 162686, 243374, 644474, 839354, 879941
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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EXAMPLE
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a(1) = 1: L(1) for D=-4*1 ~= 0.785398... = Pi/4.
a(2) = 2: L(1) for D=-4*2 ~= 1.11072073... = Pi/(2*sqrt(2)), a(2) > a(1);
L(1) for D=-4*3 ~= 0.90689..., L(1) for D=-4*4 ~= 0.785398..., both < a(2);
a(3) = 5: L(1) for D=-4*5 = 1.40496..., a(3) > a(2).
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CROSSREFS
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Cf. A331949, which has almost identical terms.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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New title, a(1) prepended, missing term 23201 and a(29)-a(33) from Hugo Pfoertner, Feb 02 2020
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STATUS
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approved
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