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A003246 Discriminants of real quadratic Euclidean fields (a finite sequence).
(Formerly M3778)
5
5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 41, 44, 57, 73, 76 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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

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

Table of n, a(n) for n=1..16.

S. R. Finch, Class number theory [Cached copy, with permission of the author]

Erich Kaltofen and Heinrich Rolletschek, Computing greatest common divisors and factorizations in quadratic number fields, Mathematics of Computation 53.188 (1989): 697-720. See page 698.

A. M. Odlyzko, Letters to N. J. A. Sloane Feb 1974

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

Index entries for sequences related to quadratic fields

FORMULA

A003246 = 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

MATHEMATICA

A003174 = {2, 3, 5, 6, 7, 11, 13, 17, 19, 21, 29, 33, 37, 41, 57, 73}; Sort[ NumberFieldDiscriminant /@ Sqrt[A003174]] (* Jean-Fran├žois Alcover, Jul 18 2012 *)

PROG

(PARI) for(n=1, 99, is_A003174(n) && print1(quaddisc(n)", ")) \\ M. F. Hasler, Jan 26 2014

CROSSREFS

Cf. A003174.

Sequence in context: A133315 A003658 A003656 * A143748 A124378 A066299

Adjacent sequences:  A003243 A003244 A003245 * A003247 A003248 A003249

KEYWORD

fini,full,nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 18 13:38 EST 2019. Contains 319271 sequences. (Running on oeis4.)