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Discriminants of real quadratic fields with narrow class number 1.
(Formerly M3782)
2

%I M3782 #18 Jul 20 2022 08:48:02

%S 5,8,13,17,29,37,41,53,61,73,89,97,101,109,113,137,149,157,173,181,

%T 193,197,233,241,269,277,281,293,313,317,337,349,353,373,389,397,409,

%U 421,433,449,457,461,509,521,541,557,569,593,601,613,617,641,653,661,673

%N Discriminants of real quadratic fields with narrow class number 1.

%C Or, positive fundamental discriminants with form class number 1.

%C All terms except 8 are primes congruent to 1 modulo 4. - _Jianing Song_, Jul 20 2022

%D D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.

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

%H Ezra Brown, <a href="https://doi.org/10.1090/S0002-9947-1974-0364172-9">Class numbers of real quadratic number fields</a>, Trans. Amer. Math. Soc. 190 (1974), 99-107.

%H Charles Delorme and Guillermo Pineda-Villavicencio, <a href="http://www.emis.de/journals/JIS/VOL18/Pineda/pin2.pdf">Quadratic Form Representations via Generalized Continuants</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.4.

%o (PARI) isA003655(n) = (n==8) || (isprime(n) && (n%4==1) && (qfbclassno(n)==1)) \\ _Jianing Song_, Jul 20 2022

%Y Equals {8} U (A003656 intersect A002144).

%Y Equals A003656 \ A327297.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, _Mira Bernstein_

%E Better definition from _David Brink_, Dec 30 2007, Jan 01 2008