%I M3778 #60 Aug 01 2024 09:24:08
%S 5,8,12,13,17,21,24,28,29,33,37,41,44,57,73,76
%N Discriminants of real quadratic norm-Euclidean fields (a finite sequence).
%C 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
%D W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 2, p. 57.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 294.
%H S. R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%H Erich Kaltofen and Heinrich Rolletschek, <a href="https://doi.org/10.1090/S0025-5718-1989-0982367-2">Computing greatest common divisors and factorizations in quadratic number fields</a>, Mathematics of Computation 53.188 (1989): 697-720. See page 698.
%H A. M. Odlyzko, <a href="/A003246/a003246.pdf">Letters to N. J. A. Sloane Feb 1974</a>
%H P. Samuel, <a href="http://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/PierreSamuel.pdf">Unique factorization</a>, Amer. Math. Monthly 75 (1968), 945-952.
%H Peter J. Weinberger, <a href="https://www.semanticscholar.org/paper/On-Euclidean-rings-of-algebraic-integers-Weinberger/3a6a7e93107dd467c87d2c60ae526ccdd34c8120">On Euclidean rings of algebraic integers</a>, Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), pp. 321-332.
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%F 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
%t 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 *)
%o (PARI) for(n=1,99,is_A003174(n) && print1(quaddisc(n)",")) \\ _M. F. Hasler_, Jan 26 2014
%Y Cf. A003174, A003656.
%K fini,full,nonn,nice
%O 1,1
%A _N. J. A. Sloane_