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%I #48 Aug 29 2018 05:01:24
%S 7,13,31,307,1723,3541,5113,8011,10303,17293,28057,30103,86143,147073,
%T 459007,492103,552793,579883,598303,684757,704761,735307,830833,
%U 1191373,1204507,1353733,1395943,1424443,1482307,1886503,2037757
%N Primes of the form p^2 + p + 1 when p is prime.
%C Also primes in A001001. - _Philippe Deléham_, Feb 21 2004
%C 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
%C Also, primes in A060800. - _Zak Seidov_, Mar 21 2014
%C Also subsequence of A002061, A193574. - _Hartmut F. W. Hoft_, May 05 2017
%C 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
%H Zak Seidov, <a href="/A053183/b053183.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A053182(n)^2 + A053182(n) + 1.
%t a053183[n_] := Select[Map[Prime[#]^2 + Prime[#] + 1&, Range[n]], PrimeQ]
%t a053183[225] (* data *) (* _Hartmut F. W. Hoft_, May 05 2017 *)
%t Select[Table[p^2+p+1,{p,Prime[Range[300]]}],PrimeQ] (* _Harvey P. Dale_, Aug 15 2017 *)
%Y Cf. A002383, A002384, A023195, A053182, A060800, A065764, A085104, A182253, A185632.
%Y Cf. A002061, A193574. - _Hartmut F. W. Hoft_, May 05 2017
%K easy,nonn
%O 1,1
%A _Enoch Haga_, Mar 01 2000
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