A262203 Primes of the form k*(k+2)/3 - 3, k>2.
2, 5, 13, 37, 53, 173, 277, 317, 557, 613, 733, 797, 1237, 1493, 1973, 2293, 3533, 4253, 4877, 5717, 9293, 9973, 12157, 12413, 14557, 16573, 17477, 19037, 20333, 22013, 23053, 26317, 26693, 30197, 32237, 32653, 33493, 37853, 40597, 44893, 50957, 53597, 54133
Offset: 1
Examples
a(1) = 2 because 2*3 + 10 = 16, which is a square. a(1) = 2 because 3*(3 + 2)/3 - 3 = 2 is prime.
Programs
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Magma
[a: k in [2..250] | IsPrime(a) where a is k*(k+2) div 3 - 3 ];
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Magma
[p: p in PrimesUpTo(60000) | IsSquare(3*p+10)];
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Mathematica
Select[Table[(k (k + 2))/3 - 3, {k, 2, 450}], PrimeQ] -
PARI
forprime(p=2, 1e5, if(issquare(3*p+10), print1(p , ", "))) \\ Altug Alkan, Dec 05 2015
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