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A003174 Real quadratic Euclidean fields (a finite sequence).
(Formerly M0619)
3
2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, 73 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

Real quadratic fields where the Euclidean algorithm applies.

REFERENCES

H. Cohn, A Second Course in Number Theory, Wiley, NY, 1962, p. 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, Uber den Euklidischen Algorithmus in quadratischen Zahlk"orpern. Ann. Acad. Sci. Fennicae Ser. A. 1. Math.-Phys., No. 41, 1-35, 1947. [Incorrectly gives 97 as a member of this sequence.]

W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 2, p. 57.

P. Samuel, Unique factorization, Amer. Math. Monthly 75 (1968), 945-952.

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

Index entries for sequences related to quadratic fields

CROSSREFS

Cf. A003246, A048981.

Sequence in context: A073485 A062101 A096530 * A166070 A053813 A116974

Adjacent sequences:  A003171 A003172 A003173 * A003175 A003176 A003177

KEYWORD

fini,nonn,full,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 15 23:53 EST 2012. Contains 205860 sequences.