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A003655 Discriminants of real quadratic fields with narrow class number 1.
(Formerly M3782)
2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Better definition from David Brink, Dec 30 2007, Jan 01 2008
STATUS
approved

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Last modified March 19 06:19 EDT 2024. Contains 370953 sequences. (Running on oeis4.)