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Primes such that the square of the sum of itself and next prime when added to 3 is a prime.
1

%I #8 Jul 18 2013 10:34:28

%S 3,23,53,83,167,211,233,251,263,331,373,443,653,727,947,977,997,1033,

%T 1117,1201,1217,1231,1237,1381,1453,1493,1621,1901,1913,1973,2069,

%U 2161,2207,2671,2837,2897,3061,3331,3691,3733,3989,4073,4253,4283,4373,4397

%N Primes such that the square of the sum of itself and next prime when added to 3 is a prime.

%C [p(i)+p(i+1)]^2+3 is a prime.

%e a(5) = 167 since (167+173)^2+3 = 340^2+3 = 115600+3 = 115603 is a prime.

%o (PARI) isok(n) = (isprime(n) && isprime(3+(n + nextprime(n+1))^2)) \\ _Michel Marcus_, Jul 18 2013

%Y Cf. A000045, A181421.

%K nonn

%O 1,1

%A _Carmine Suriano_, Oct 18 2010

%E 1201 and 1217 inserted by _R. J. Mathar_, Oct 18 2010