A212304 - OEIS

%I #16 Oct 26 2013 14:24:23

%S 5,11,53,1381,3739,6263,12799,32803,57173,177323,187573,491527,674183,

%T 1067263,1125899,1142941,1230067,1352761,1471567,1745257,1885349,

%U 2283361,2563453,2779151,3893027,4364237,5508757,6933071,7513481,7790087,8048981,9370159,11499359

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

%H K. D. Bajpai, <a href="/A212304/b212304.txt">Table of n, a(n) for n = 1..6700</a>

%e a(3) = 53 :  prime(4)^2 + 4 = 7^2 + 4 = 49 + 4 = 53 which is prime.

%e a(4) = 1381 :  prime(12)^2 + 12 = 37^2 + 12 = 1369 + 12 = 1381 which is prime.

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

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

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

%Y Cf. A000040 (prime numbers).

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

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

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

%K nonn

%O 1,1

%A _K. D. Bajpai_, Oct 24 2013