A003655 Discriminants of real quadratic fields with narrow class number 1. (Formerly M3782)

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

1,1

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

Table of n, a(n) for n=1..55.

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.

Prog

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

Crossrefs

Equals {8} U (A003656 intersect A002144).

Equals A003656 \ A327297.

Sequence in context: A314433 A314434 A003653 * A082823 A143747 A314435

Adjacent sequences: A003652 A003653 A003654 * A003656 A003657 A003658

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

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

Status

approved