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 A342691 Primes of the form (p^k)^2 + p^k + 1 with prime p and positive integer k. 3
 7, 13, 31, 73, 307, 757, 1723, 3541, 5113, 8011, 10303, 17293, 28057, 30103, 86143, 147073, 262657, 459007, 492103, 552793, 579883, 598303, 684757, 704761, 735307, 830833, 1191373, 1204507, 1353733, 1395943, 1424443, 1482307, 1772893, 1886503, 2037757, 2212657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Martin Becker, Table of n, a(n) for n = 1..20000 EXAMPLE 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. 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. PROG (PARI) for(q=2, 2048, if(isprimepower(q), m=q^2+q+1; if(isprime(m), print1(m, ", ")))) CROSSREFS Contains A053183 and A066101. Intersection of A335865 and A000040 minus {3}. Cf. A342690, A344448. Sequence in context: A174217 A040061 A289123 * A215932 A091432 A102002 Adjacent sequences: A342688 A342689 A342690 * A342692 A342693 A342694 KEYWORD nonn AUTHOR Martin Becker, May 18 2021 STATUS approved

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Last modified December 4 06:57 EST 2023. Contains 367557 sequences. (Running on oeis4.)