A053183 Primes of the form p^2 + p + 1 when p is prime.

7, 13, 31, 307, 1723, 3541, 5113, 8011, 10303, 17293, 28057, 30103, 86143, 147073, 459007, 492103, 552793, 579883, 598303, 684757, 704761, 735307, 830833, 1191373, 1204507, 1353733, 1395943, 1424443, 1482307, 1886503, 2037757

Offset: 1

Author

Enoch Haga, Mar 01 2000

Keywords

• easy
• nonn

Comments

Also primes in A001001. - Philippe Deléham, Feb 21 2004

This sequence is a subsequence of A002383. These numbers are repunit primes 111_n, so they are Brazilian primes belonging to A085104. - Bernard Schott, Dec 21 2012

Also, primes in A060800. - Zak Seidov, Mar 21 2014

Also subsequence of A002061, A193574. - Hartmut F. W. Hoft, May 05 2017

As p^2 + p + 1 is the sum of divisors of p^2 for any prime p, this is a subsequence of A023195. - Peter Munn, Feb 16 2018

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002383, A002384, A023195, A053182, A060800, A065764, A085104, A182253, A185632.

Cf. A002061, A193574. - Hartmut F. W. Hoft, May 05 2017

Programs

Mathematica

a053183[n_] := Select[Map[Prime[#]^2 + Prime[#] + 1&, Range[n]], PrimeQ]
a053183[225] (* data *) (* Hartmut F. W. Hoft, May 05 2017 *)
Select[Table[p^2+p+1,{p,Prime[Range[300]]}],PrimeQ] (* Harvey P. Dale, Aug 15 2017 *)

Formula

a(n) = A053182(n)^2 + A053182(n) + 1.