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A309520 Primes p for which h1(p)/G(p) has a record value. 0
3, 5, 7, 11, 23, 73, 89, 179, 233, 761, 1451, 2741, 4391, 5231, 6766811 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

h1 is given by A000927, and G(p) = 2*p*(p/(4*Pi^2))^((p-1)/4).

a(1) to a(12) come from Fung et al.

a(13) and a(14) come from Shokrollahi.

a(15) comes from Languasco et al.

LINKS

Table of n, a(n) for n=1..15.

Gilbert Fung, Andrew Granville, Hugh C. Williams, Computation of the first factor of the class number of cyclotomic fields, Journal of Number Theory, Volume 42, Issue 3, November 1992, Pages 297-312. See Table IV A p. 304.

Alessandro Languasco, Pieter Moree, Sumaia Saad Eddin, Alisa Sedunova, Computation of the Kummer ratio of the class number for prime cyclotomic fields, arXiv:1908.01152 [math.NT], 2019.

M. A. Shokrollahi, Relative class number of imaginary Abelian fields of prime conductor below 10000, Math. Comp. 68 (1999), 1717-1728. See Table 4 p. 1726.

PROG

(PARI) h1(p) = if (p<5, 1, abs( matdet(matrix((p-1)/2-2, (p-1)/2-2, i, j, ((i+2)*(j+2))\p - ((i+1)*(j+2))\p)) )); \\ A000927

G(p) = 2*p*(p/(4*Pi^2))^((p-1)/4);

lista(nn) = {my(m = 0, nm); for (n=2, nn, p = prime(n); if ((nm = h1(p)/G(p)) > m, print1(p, ", "); m = nm); ); }

CROSSREFS

Cf. A000927 (h1), A073010 (value for p=3).

Sequence in context: A227240 A226017 A303705 * A265687 A023368 A295973

Adjacent sequences:  A309517 A309518 A309519 * A309521 A309522 A309523

KEYWORD

nonn,more

AUTHOR

Michel Marcus, Aug 06 2019

STATUS

approved

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Last modified March 4 02:31 EST 2021. Contains 341773 sequences. (Running on oeis4.)