A072902 Nonprime numbers m such that the discriminant of the quadratic field Q(sqrt(m)) equals m.

1, 8, 12, 21, 24, 28, 33, 40, 44, 56, 57, 60, 65, 69, 76, 77, 85, 88, 92, 93, 104, 105, 120, 124, 129, 133, 136, 140, 141, 145, 152, 156, 161, 165, 168, 172, 177, 184, 185, 188, 201, 204, 205, 209, 213, 217, 220, 221, 232, 236, 237, 248, 249, 253, 264, 265, 268

Offset

1,2

Comments

A subset of the nonprime numbers (A018252).

Positive fundamental discriminants (A003658) that are not Pythagorean primes (A002144). - Paul Muljadi, Mar 30 2008

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) appears to be asymptotic to C*n with C = 3.91... .

Mathematica

FundamentalDiscriminantQ[d_] := Module[{m, mod = Mod[d, 4]}, If[mod > 1, Return[False]]; If[mod == 1, Return[ SquareFreeQ[d] && d != 1]]; m = d/4; Return[ SquareFreeQ[m] && Mod[m, 4] > 1]]; Join[{1}, Select[ Range[270], !PrimeQ[#] && FundamentalDiscriminantQ[#]& ]] (* Jean-François Alcover, Jun 05 2012, after Eric W. Weisstein *)

Prog

(PARI) isok(m) = !isprime(m) && (quaddisc(m) == m); \\ Michel Marcus, Feb 18 2021

Crossrefs

Cf. A037449.

Cf. A002144, A018252, A003658.

Sequence in context: A354069 A350615 A300065 * A269705 A189322 A105571

Adjacent sequences: A072899 A072900 A072901 * A072903 A072904 A072905

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 10 2002

Status

approved