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%I #47 Aug 18 2021 09:30:27
%S -11,-7,-3,-2,-1,2,3,5,6,7,11,13,17,19,21,29,33,37,41,57,73
%N Squarefree values of n for which the quadratic field Q[ sqrt(n) ] is norm-Euclidean.
%C These are norm-Euclidean fields, excluding for instance Q[sqrt(69)] which is Euclidean but not for norm. - _Marc A. A. van Leeuwen_, Feb 15 2011
%D H. Cohn, A Second Course in Number Theory, Wiley, NY, 1962, pp. 107, 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 H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 294.
%H Alexander Bogomolny, <a href="http://www.cut-the-knot.org/arithmetic/int_domain4.shtml">Strange Integers</a>
%H Kyle Bradford and Eugen J. Ionascu, <a href="http://arxiv.org/abs/1405.4025">Unit Fractions in Norm-Euclidean Rings of Integers</a>, arXiv:1405.4025 [math.NT], May 2014 (see p. 3).
%H Eugen J. Ionascu and Kyle Bradford, <a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/368">Unit Fractions in Norm-Euclidean Rings of Integers</a>, Acta Mathematica Universitatis Comenianae, 86(1), 127-141.
%H Pierre Samuel, <a href="http://www.jstor.org/stable/2315529">Unique factorization</a>, Amer. Math. Monthly 75 (1968), 945-952.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuadraticField.html">Quadratic Field</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Norm-Euclidean_field">Norm-Euclidean field</a>.
%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%F a(n) = -A003173(6-n) = -A263465(6-n) for n = 1, 2, 3, 4, 5. - _Jonathan Sondow_, Dec 09 2015
%p select(t -> traperror(numtheory:-factorEQ(-1,t)) <> lasterror, [$-11..77]); # _Robert Israel_, Jul 20 2016
%Y Cf. A003173, A003174, A263465.
%K fini,sign,full,nice
%O 1,1
%A _N. J. A. Sloane_, _Jud McCranie_
%E Name corrected by _Marc A. A. van Leeuwen_, Feb 15 2011
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