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%I M0619 #60 Jul 18 2022 22:47:09
%S 2,3,5,6,7,11,13,17,19,21,29,33,37,41,57,73
%N Positive integers D such that Q[sqrt(D)] is a quadratic field which is norm-Euclidean.
%C These integers yield norm-Euclidean real quadratic fields. There are other positive integers, e.g., D=14 or D=69, for which Q[sqrt(D)] is Euclidean, but for a Euclidean function different from the field norm.
%C For further references see sequence A048981 which also lists negative D corresponding to (complex) norm-Euclidean fields. - _M. F. Hasler_, Jan 26 2014
%D H. Cohn, A Second Course in Number Theory, Wiley, NY, 1962, p. 109.
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 213.
%D K. Inkeri, Über den Euklidischen Algorithmus in quadratischen Zahlkörpern. Ann. Acad. Sci. Fennicae Ser. A. 1. Math.-Phys., No. 41, 1-35, 1947. [Incorrectly gives 97 as a member of this sequence.]
%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 H. Chatland and H. Davenport, <a href="https://doi.org/10.4153/CJM-1950-026-7">Euclid's algorithm in real quadratic fields</a>, Canadian J. Math. 2, (1950), 289-296.
%H S. R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%H Pierre Samuel, <a href="http://www.jstor.org/stable/2315529">Unique factorization</a>, Amer. Math. Monthly 75 (1968), 945-952.
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%F a(n) = A048981(n+5). - _M. F. Hasler_, Jan 26 2014
%o (PARI) is_A003174(n) = bittest(9444877083272958060780,n) \\ _M. F. Hasler_, Jan 26 2014
%Y Cf. A003173, A003246, A048981, A187776, A263465.
%K fini,nonn,full,nice
%O 1,1
%A _N. J. A. Sloane_
%E Definition corrected and comment rephrased by _M. F. Hasler_, Jan 26 2014
%E Definition corrected by _Jonathan Sondow_, Oct 19 2015
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