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Largest prime == 7 (mod 8) with class number 2n+1.
(Formerly M4402 N1857)
3

%I M4402 N1857 #21 Aug 06 2022 07:17:52

%S 7,31,127,487,1423,1303,2143,2647,4447,5527,5647,6703,5503,11383,8863,

%T 13687,13183,12007,22807,18127,21487,22303,29863,25303,27127

%N Largest prime == 7 (mod 8) with class number 2n+1.

%C Apr 14 2008: _David Broadhurst_ says: I computed class numbers for prime discriminants with |D| < 10^9, but stopped when the first case with |D| > 5*10^8 was observed. That factor of 2 seems to me to be a reasonable margin of error, when you look at the pattern of what is included.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David Broadhurst, <a href="/A002147/b002147.txt">Table of n, a(n) for n = 0..2246</a> (conjectural; see comment).

%H D. Shanks, <a href="https://doi.org/10.1090/S0025-5718-70-99853-4">Review of R. B. Lakein and S. Kuroda, Tables of class numbers h(-p) for fields Q(sqrt(-p)), p <= 465071</a>, Math. Comp., 24 (1970), 491-492.

%Y Cf. A002146.

%K nonn

%O 0,1

%A _N. J. A. Sloane_