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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A045331 Primes congruent to {1, 2, 3} mod 6; or, -3 is a square mod p. 13
2, 3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

-3 is a quadratic residue mod a prime p iff p is in this sequence.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Prime[Range[200]], MemberQ[{1, 2, 3}, Mod[#, 6]]&]  (* Harvey P. Dale, Mar 31 2011 *)

Join[{2, 3}, Select[Range[7, 10^3, 6], PrimeQ]] (* Zak Seidov, May 20 2011 *)

PROG

(PARI) select(primes(100), n->n%6<5) \\ old versions

select(n->n%6<5, primes(100)) \\ new versions

\\ Charles R Greathouse IV, May 20, 2011

(MAGMA) [p: p in PrimesUpTo(700) | p mod 6 in [1, 2, 3]]; // Vincenzo Librandi, Aug 08 2012

(Haskell)

a045331 n = a045331_list !! (n-1)

a045331_list = filter ((< 4) . (`mod` 6)) a000040_list

-- Reinhard Zumkeller, Jan 15 2013

CROSSREFS

Apart from initial term, same as A007645; apart from initial two terms, same as A002476.

Cf. A002313, A033203, A038873, A038874, A057128.

Subsequence of A047246.

Sequence in context: A051484 A101415 A210393 * A053613 A013645 A130272

Adjacent sequences:  A045328 A045329 A045330 * A045332 A045333 A045334

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Henry Bottomley, Aug 10 2000

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 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)