A342690 Prime powers q in A246655 such that q^2 + q + 1 is prime.

2, 3, 5, 8, 17, 27, 41, 59, 71, 89, 101, 131, 167, 173, 293, 383, 512, 677, 701, 743, 761, 773, 827, 839, 857, 911, 1091, 1097, 1163, 1181, 1193, 1217, 1331, 1373, 1427, 1487, 1559, 1583, 1709, 1811, 1847, 1931, 1973, 2129, 2273, 2309, 2339, 2411, 2663

Offset: 1

Author

Martin Becker, May 18 2021

Keywords

• nonn

Comments

Also, prime powers q = p^(3^k) with prime p and nonnegative integer k and the property that q^2 + q + 1 is prime, since the exponent must be a power of 3, from the theory of cyclotomic polynomials. 17^(3^7) is in the sequence, generating a 5382-digit prime.

Examples

			5 = 5^1 is a term: 5^2 + 5 + 1 = 31 is prime.
8 = 2^3 is a term: 8^2 + 8 + 1 = 73 is prime.
		

Links

• Martin Becker, Table of n, a(n) for n = 1..20000

Crossrefs

Intersection of A246655 and A002384.

Cf. A342691, A344448.

Programs

Mathematica

Select[Range@2000,PrimePowerQ@#&&PrimeQ[#^2+#+1]&] (* Giorgos Kalogeropoulos, May 18 2021 *)

PARI

N=50; i=0; a=vector(N); for(q=2, oo, if(isprimepower(q) && isprime(q^2+q+1), i+=1; a[i]=q; if(i==N, break))); a