login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072902 Nonprime numbers m such that the discriminant of the quadratic field Q(sqrt(m)) equals m. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..57.

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: A258848 A072843 A300065 * A269705 A189322 A105571

Adjacent sequences:  A072899 A072900 A072901 * A072903 A072904 A072905

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Aug 10 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 04:21 EST 2021. Contains 349567 sequences. (Running on oeis4.)