OFFSET
1,1
COMMENTS
Euclidean fields that are not norm-Euclidean, such as Q(sqrt(14)) and Q(sqrt(69)), are not included. Actually, assuming GCH, a real quadratic field is Euclidean if and only if it is a PID (equivalently, if and only if it is a UFD). - Jianing Song, Jun 09 2022
REFERENCES
W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 2, p. 57.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 294.
LINKS
S. R. Finch, Class number theory [Cached copy, with permission of the author]
Erich Kaltofen and Heinrich Rolletschek, Computing greatest common divisors and factorizations in quadratic number fields, Mathematics of Computation 53.188 (1989): 697-720. See page 698.
A. M. Odlyzko, Letters to N. J. A. Sloane Feb 1974
P. Samuel, Unique factorization, Amer. Math. Monthly 75 (1968), 945-952.
Peter J. Weinberger, On Euclidean rings of algebraic integers, Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), pp. 321-332.
FORMULA
Equals A037449(A003174) as a set, not composition of functions (values are sorted by size; it turns out that a(n) is different from A037449(A003174(n)) for all n=1,...,16). - M. F. Hasler, Jan 26 2014
MATHEMATICA
A003174 = {2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, 73}; Sort[ NumberFieldDiscriminant /@ Sqrt[A003174]] (* Jean-François Alcover, Jul 18 2012 *)
PROG
(PARI) for(n=1, 99, is_A003174(n) && print1(quaddisc(n)", ")) \\ M. F. Hasler, Jan 26 2014
CROSSREFS
KEYWORD
fini,full,nonn,nice
AUTHOR
STATUS
approved