cp's OEIS Frontend

A309520 Primes p for which h1(p)/G(p) has a record value.

%I A309520 #52 Sep 27 2024 08:31:49
%S A309520 3,5,7,11,23,73,89,179,233,761,1451,2741,4391,5231,42611,198221,
%T A309520 305741,6766811,1326662801,1979990861,4735703723,9697282541,
%U A309520 35285447111,45169368641,169684421321,187946428721
%N A309520 Primes p for which h1(p)/G(p) has a record value.
%C A309520 h1 is given by A000927, and G(p) = 2*p*(p/(4*Pi^2))^((p-1)/4).
%C A309520 a(1)-a(12) from Fung et al., a(13)-a(14) from Shokrollahi, a(15)-a(17) from Broadhurst, a(18) from Languasco et al. and Broadhurst, a(19)-a(26) from Broadhurst.
%H A309520 David Broadhurst, <a href="https://www.dei.unipd.it/~languasco/Broadhurst-OEIS/Broadhurst-OEIS.txt">Kummer ratio champions with p < 10^12</a>, July 22 2021.
%H A309520 Gilbert Fung, Andrew Granville and Hugh C. Williams, <a href="https://doi.org/10.1016/0022-314X(92)90095-7">Computation of the first factor of the class number of cyclotomic fields</a>, Journal of Number Theory, Volume 42, Issue 3, November 1992, Pages 297-312. See Table IV A p. 304.
%H A309520 Alessandro Languasco, Pieter Moree, Sumaia Saad Eddin and Alisa Sedunova, <a href="https://arxiv.org/abs/1908.01152">Computation of the Kummer ratio of the class number for prime cyclotomic fields</a>, arXiv:1908.01152 [math.NT], 2019.
%H A309520 M. A. Shokrollahi, <a href="https://doi.org/10.1090/S0025-5718-99-01139-4">Relative class number of imaginary Abelian fields of prime conductor below 10000</a>, Math. Comp. 68 (1999), 1717-1728. See Table 4 p. 1726.
%o A309520 (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
%o A309520 G(p) = 2*p*(p/(4*Pi^2))^((p-1)/4);
%o A309520 lista(nn) = {my(m = 0, nm); for (n=2, nn, p = prime(n); if ((nm = h1(p)/G(p)) > m, print1(p, ", "); m = nm););}
%Y A309520 Cf. A000927 (h1), A073010 (value for p=3).
%K A309520 nonn,more
%O A309520 1,1
%A A309520 _Michel Marcus_, Aug 06 2019
%E A309520 Missing terms 42611, 198221, 305741 and terms larger than 6766811 added by _Alessandro Languasco_ on behalf of _David Broadhurst_, Jul 24 2021