A003655 Discriminants of real quadratic fields with narrow class number 1.

5, 8, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 233, 241, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 593, 601, 613, 617, 641, 653, 661, 673

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

Comments

Or, positive fundamental discriminants with form class number 1.

All terms except 8 are primes congruent to 1 modulo 4. - Jianing Song, Jul 20 2022

References

• D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Ezra Brown, Class numbers of real quadratic number fields, Trans. Amer. Math. Soc. 190 (1974), 99-107.
• Charles Delorme and Guillermo Pineda-Villavicencio, Quadratic Form Representations via Generalized Continuants, Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.4.

Crossrefs

Equals {8} U (A003656 intersect A002144).

Equals A003656 \ A327297.

Programs

PARI

isA003655(n) = (n==8) || (isprime(n) && (n%4==1) && (qfbclassno(n)==1)) \\ Jianing Song, Jul 20 2022

Extensions

Better definition from David Brink, Dec 30 2007, Jan 01 2008