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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
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(n->n%6<5, primes(100)) \\ 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.
Subsequence of A047246.
Sequence in context: A051484 A101415 A210393 * A053613 A013645 A130272
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Henry Bottomley, Aug 10 2000
STATUS
approved

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Last modified May 19 14:15 EDT 2024. Contains 372697 sequences. (Running on oeis4.)