

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
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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 !! (n1)
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



