A003419 - OEIS

A003419

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>0} Kronecker(D,k)/k.
(Formerly M2102)

1, 2, 17, 167, 227, 362, 398, 331427, 430022, 737183, 800663, 821498, 1475858, 2271407, 3009173, 5417453

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OFFSET

1,2

COMMENTS

The terms a(2)-a(7) are given in Shanks's Table 4 "Lochamps, 4M = Discriminant". This table gives some values of L(1) for larger discriminants, e.g., L(1) = 0.2510... for D = 4*4813372912697. In comparison, L(1) = 0.28422 for D = 4*a(16) = 4*5417453. - Hugo Pfoertner, Feb 07 2020

REFERENCES

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).

LINKS

Table of n, a(n) for n=1..16.

D. Shanks, Systematic examination of Littlewood's bounds on L(1,chi), Proc. Sympos. Pure Math., 24 (1973). Amer. Math. Soc. (Annotated scanned copy)

CROSSREFS

Cf. A003420, A003421, A003521.

Sequence in context: A178806 A197864 A231616 * A126109 A046909 A041879

Adjacent sequences: A003416 A003417 A003418 * A003420 A003421 A003422

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

New title, a(1) prepended, and a(8)-a(13) from Hugo Pfoertner, Feb 04 2020

a(14)-a(15) from Hugo Pfoertner, Feb 05 2020

a(16) from Hugo Pfoertner, Feb 07 2020

STATUS

approved