A063784 -id:A063784 - cp's OEIS frontend

A066101 Duplicate of A063784.

73, 757, 1772893, 48551233240513, 378890487846991, 3156404483062657, 17390284913300671, 280343912759041771, 319913861581383373, 487014306953858713, 7824668707707203971, 8443914727229480773, 32564717507686012813, 48095468363380957093, 54811417636756749151

Offset: 1

dead

Previous name: Primes of the form q = p^6 + p^3 + 1 = sigma_3(p^2), where p is prime.

			73 = 64 + 8 + 1, 757 = 729 + 27 + 1, etc.

A342691 Primes of the form (p^k)^2 + p^k + 1 with prime p and positive integer k.

Original entry on oeis.org

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

Offset: 1

Martin Becker, May 18 2021

nonn

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.

			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.

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

Contains A053183 and A063784.
Intersection of A335865 and A000040 minus {3}.
Cf. A342690, A344448.

Select[Table[q^2 + q + 1, {q, Select[Range[1500], PrimePowerQ[#] &]}], PrimeQ] (* Amiram Eldar, Aug 16 2024 *)

for(q=2,2048,if(isprimepower(q),m=q^2+q+1;if(isprime(m),print1(m, ", "))))

cp's OEIS Frontend

A066101 Duplicate of A063784.

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A342691 Primes of the form (p^k)^2 + p^k + 1 with prime p and positive integer k.

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