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A053183 Primes of the form p^2 + p + 1 when p is prime. 18
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

FORMULA

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

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 *)

CROSSREFS

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

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

Sequence in context: A195353 A342184 A247178 * A247955 A026318 A331960

Adjacent sequences:  A053180 A053181 A053182 * A053184 A053185 A053186

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Mar 01 2000

STATUS

approved

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)