

A048981


Squarefree values of n for which the quadratic field Q[ sqrt(n) ] is normEuclidean.


6



11, 7, 3, 2, 1, 2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, 73
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OFFSET

1,1


COMMENTS

These are normEuclidean fields, excluding for instance Q[sqrt(69)] which is Euclidean but not for norm.  Marc A. A. van Leeuwen, Feb 15 2011


REFERENCES

H. Cohn, A Second Course in Number Theory, Wiley, NY, 1962, pp. 107, 109.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 213.
K. Inkeri, Über den Euklidischen Algorithmus in quadratischen Zahlkörpern. Ann. Acad. Sci. Fennicae Ser. A. 1. Math.Phys., No. 41, 135, 1947. [Incorrectly gives 97 as a member of this sequence.]
W. J. LeVeque, Topics in Number Theory. AddisonWesley, Reading, MA, 2 vols., 1956, Vol. 2, p. 57.
H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 294.


LINKS

Table of n, a(n) for n=1..21.
Alexander Bogomolny, Strange Integers
Kyle Bradford, Eugen J. Ionascu, Unit Fractions in NormEuclidean Rings of Integers, arXiv:1405.4025 [math.NT], May 2014 (see p. 3).
Pierre Samuel, Unique factorization, Amer. Math. Monthly 75 (1968), 945952.
Eric Weisstein's World of Mathematics, Quadratic Field
Wikipedia, NormEuclidean field.
Index entries for sequences related to quadratic fields


FORMULA

a(n) = A003173(6n) = A263465(6n) for n = 1, 2, 3, 4, 5.  Jonathan Sondow, Dec 09 2015


MAPLE

select(t > traperror(numtheory:factorEQ(1, t)) <> lasterror, [$11..77]); # Robert Israel, Jul 20 2016


CROSSREFS

Cf. A003173, A003174, A263465.
Sequence in context: A010185 A005603 A109828 * A132361 A236546 A155914
Adjacent sequences: A048978 A048979 A048980 * A048982 A048983 A048984


KEYWORD

fini,sign,full,nice


AUTHOR

N. J. A. Sloane, Jud McCranie


EXTENSIONS

Name corrected by Marc A. A. van Leeuwen, Feb 15 2011


STATUS

approved



