A212304 Primes of the form prime(n)^2 + n.

5, 11, 53, 1381, 3739, 6263, 12799, 32803, 57173, 177323, 187573, 491527, 674183, 1067263, 1125899, 1142941, 1230067, 1352761, 1471567, 1745257, 1885349, 2283361, 2563453, 2779151, 3893027, 4364237, 5508757, 6933071, 7513481, 7790087, 8048981, 9370159, 11499359

Offset: 1

Author

K. D. Bajpai, Oct 24 2013

Keywords

• nonn

Examples

			a(3) = 53 :  prime(4)^2 + 4 = 7^2 + 4 = 49 + 4 = 53 which is prime.
a(4) = 1381 :  prime(12)^2 + 12 = 37^2 + 12 = 1369 + 12 = 1381 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..6700

Crossrefs

Cf. A000040 (prime numbers).

Cf. A184935 (primes: k^2 + prime(k)).

Cf. A188831 (primes: k^2 - prime(k)).

Cf. A229203 (primes: k^3 - prime(k)).

Programs

Maple

with(numtheory):KD := proc() local a; a:= (ithprime(k)^2+k); if isprime(a) then RETURN (a); fi; end: seq(KD(),k=1..1000);

Mathematica

Select[Table[Prime[k]^2 + k, {k, 1000}], PrimeQ]

PARI

for(k=1, 10^5, if(ispseudoprime(KD=((prime(k)^2+k))), print1(KD", ")));