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%I #41 Aug 16 2024 21:20:20
%S 7,13,31,73,307,757,1723,3541,5113,8011,10303,17293,28057,30103,86143,
%T 147073,262657,459007,492103,552793,579883,598303,684757,704761,
%U 735307,830833,1191373,1204507,1353733,1395943,1424443,1482307,1772893,1886503,2037757,2212657
%N Primes of the form (p^k)^2 + p^k + 1 with prime p and positive integer k.
%C Also, primes of the form (p^3^m)^2 + p^3^m + 1 with prime p and nonnegative integer m, since k must be a power of 3, from the theory of cyclotomic polynomials.
%H Martin Becker, <a href="/A342691/b342691.txt">Table of n, a(n) for n = 1..20000</a>
%e 31 = (5^1)^2 + 5^1 + 1 is in the sequence as 31 is prime and 5 is prime and 1 is a positive integer.
%e 73 = (2^3)^2 + 2^3 + 1 is in the sequence as it is prime and 2 is prime and 3 is a positive integer.
%t Select[Table[q^2 + q + 1, {q, Select[Range[1500], PrimePowerQ[#] &]}], PrimeQ] (* _Amiram Eldar_, Aug 16 2024 *)
%o (PARI) for(q=2,2048,if(isprimepower(q),m=q^2+q+1;if(isprime(m),print1(m, ", "))))
%Y Contains A053183 and A063784.
%Y Intersection of A335865 and A000040 minus {3}.
%Y Cf. A342690, A344448.
%K nonn
%O 1,1
%A _Martin Becker_, May 18 2021
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