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Harvey P. Dale, <a href="/A215429/b215429_1.txt">Table of n, a(n) for n = 1..1000</a>
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Harvey P. Dale, <a href="/A215429/b215429_1.txt">Table of n, a(n) for n = 1..1000</a>
Select[(#+1)/6&/@Select[Range[3000]^2+1, PrimeQ], PrimeQ] (* Harvey P. Dale, May 07 2017 *)
approved
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allocated for Michel LagneauPrimes of the form (n^2+2)/6 where n^2+1 is prime.
3, 17, 43, 67, 113, 523, 2017, 2243, 4817, 8363, 9283, 16433, 17713, 19267, 30817, 56843, 81667, 97283, 141067, 149153, 185153, 203873, 271363, 279073, 329473, 398353, 400417, 455953, 472643, 481667, 513923, 519793, 530443, 549643, 670673, 684113, 746243
1,1
The corresponding n are in A215248.
3 is in the sequence because, for n = 4, 4^2 + 1 = 17 and (4^2 + 2)/6 = 3 are primes.
lst={}; Do[ p=n^2+ 1; q=(p+1)/6; If[PrimeQ[p]&&PrimeQ[q], AppendTo[lst, q]], {n, 0, 2500}]; lst
allocated
nonn
Michel Lagneau, Aug 10 2012
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allocated for Michel Lagneau
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Primes congruent to {0, 2, 4, 5, 6} mod 17.
2, 5, 17, 19, 23, 53, 73, 89, 107, 157, 191, 193, 223, 227, 257, 277, 293, 311, 359, 379, 397, 431, 461, 463, 499, 563, 599, 601, 617, 631, 701, 719, 733, 769, 787, 821, 839, 907, 937, 941, 971, 991, 1009, 1039, 1093, 1109, 1213, 1229, 1277, 1279, 1297
1,1
Vincenzo Librandi, <a href="/A215429/b215429.txt">Table of n, a(n) for n = 1..1000</a>
Select[Prime[Range[300]], MemberQ[{0, 2, 4, 5, 6}, Mod[#, 17]]&]
(MAGMA) [p: p in PrimesUpTo(1300) | p mod 17 in [0, 2, 4, 5, 6]];
nonn,easy,changed
recycled
Vincenzo Librandi, Aug 10 2012
proposed
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