login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A039957 Squarefree numbers congruent to 3 mod 4. 10
3, 7, 11, 15, 19, 23, 31, 35, 39, 43, 47, 51, 55, 59, 67, 71, 79, 83, 87, 91, 95, 103, 107, 111, 115, 119, 123, 127, 131, 139, 143, 151, 155, 159, 163, 167, 179, 183, 187, 191, 195, 199, 203, 211, 215, 219, 223, 227, 231, 235, 239, 247, 251, 255 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Negative of odd fundamental discriminants D := b^2-4*a*c<0 of definite integer binary quadratic forms F=a*x^2+b*x*y+c*y^2. See Buell reference pp. 224-230. See 4*A089269 for the even case and A003657 for combined even and odd numbers. - Wolfdieter Lang, Nov 07 2003

REFERENCES

R. A. Mollin, Quadratics, CRC Press, 1996, Tables B1-B3.

D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

MATHEMATICA

fQ[n_] := SquareFreeQ[n] && Mod[n, 4] == 3; Select[ Range@ 258, fQ] (* Robert G. Wilson v, Mar 02 2011 *)

Select[Range[3, 300, 4], SquareFreeQ] (* Harvey P. Dale, Mar 08 2015 *)

PROG

(MAGMA) [4*n+3: n in [0..63] | IsSquarefree(4*n+3)];  // Bruno Berselli, Mar 04 2011

(Haskell)

a039957 n = a039957_list !! (n-1)

a039957_list = filter ((== 3) . (`mod` 4)) a005117_list

-- Reinhard Zumkeller, Aug 15 2011

(PARI) is(n)=n%4==3 && issquarefree(n) \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Cf. A039955, A039956.

Sequence in context: A131098 A118894 A194397 * A217332 A079422 A277675

Adjacent sequences:  A039954 A039955 A039956 * A039958 A039959 A039960

KEYWORD

nonn,easy,nice

AUTHOR

R. K. Guy

EXTENSIONS

Offset corrected

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 28 07:54 EDT 2017. Contains 284182 sequences.