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A038874
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Primes p such that 3 is a square mod p.
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10
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2, 3, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 131, 157, 167, 179, 181, 191, 193, 227, 229, 239, 241, 251, 263, 277, 311, 313, 337, 347, 349, 359, 373, 383, 397, 409, 419, 421, 431, 433, 443, 457, 467, 479, 491, 503, 541, 563, 577, 587, 599, 601
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OFFSET
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1,1
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COMMENTS
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Also primes congruent to {1, 2, 3, 11} mod 12.
The subsequence p=1 (mod 4) corresponds to A068228 and only these entries of a(n) are squares mod 3 (from the quadratic reciprocity law). - Lekraj Beedassy, Jul 21 2004
Largest prime factors of n^2-3. [From Vladimir Joseph Stephan Orlovsky, Aug 12 2009]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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lst={}; Do[AppendTo[lst, FactorInteger[n^2-3, FactorComplete->True][[ -1, 1]]], {n, 7!}]; Take[Union[lst], 66] [From Vladimir Joseph Stephan Orlovsky, Aug 12 2009]
Select[Prime[Range[250]], MemberQ[{1, 2, 3, 11}, Mod[#, 12]]&] (* Vincenzo Librandi, Aug 08 2012 *)
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PROG
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(MAGMA) [p: p in PrimesUpTo(1200) | p mod 12 in [1, 2, 3, 11]]; // Vincenzo Librandi, Aug 08 2012
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CROSSREFS
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Cf. A002313, A033203, A038873, A045331, A057125.
If the first two terms are omitted we get A097933. A040101 is another sequence.
Sequence in context: A090707 A062350 A163498 * A164624 A215819 A040101
Adjacent sequences: A038871 A038872 A038873 * A038875 A038876 A038877
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Henry Bottomley, Aug 10 2000
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STATUS
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approved
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