A227890 Primes of the form prime(k)^2 - k.

3, 7, 163, 353, 5021, 12739, 32719, 49681, 52391, 78901, 113501, 252913, 361091, 452807, 551917, 993841, 1559797, 1956979, 2193127, 3463037, 4067983, 5003837, 5138953, 6115363, 6723271, 7251857, 7447043, 7578607, 8426989, 9479801, 11295847, 12186593, 12439237

Offset: 1

Author

K. D. Bajpai, Oct 26 2013

Keywords

• nonn

Examples

			a(3)= 163: prime(6)^2 - 6= 13^2 - 6= 169 - 6= 163 which is prime.
a(4)= 353: prime(8)^2 - 8= 19^2 - 8= 361 - 8= 353 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..7200

Crossrefs

Cf. A000040 (prime numbers).

Cf. A064713 (for the integers k).

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", ")));