%I
%S 2,3,11,13,53,131,233,241,281,569,659,691,761,881,1693,2063,2411,2521,
%T 2551,2663,2729,2741,2861,3089,4021,4159,4201,4243,4423,4793,6091,
%U 7103,7229,7369,7753,7829,8053,8641,8669,9041,9059,9539,9649,9769,10513
%N First member of a prime triple in a p^2 + p  1 progression.
%C There exist no such triples of the form p^2 + p + 1 because each third member is always divisible by 3.
%C Subsequence of A053184.  _Pierre CAMI_, Sep 13 2013
%H Pierre CAMI, <a href="/A057324/b057324.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%e 2 > 2^2+21 = 5 > 5^2+51 = 29 hence the prime triple (2,5,29).
%t fmpQ[n_]:=AllTrue[NestList[#^2+#1&,n,2],PrimeQ]; Select[Prime[Range[ 1300]],fmpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 08 2019 *)
%o (PARI) is(n)=for(k=1,3,if(!isprime(n),return(0));n=n^2+n1);1 \\ _Charles R Greathouse IV_, Sep 13 2013
%Y Cf. A053184, A053185, A057325.
%K nonn
%O 1,1
%A _Patrick De Geest_, Aug 15 2000
