cp's OEIS Frontend

A252231 Primes of the form (p+q)^2 + pq, where p and q are consecutive primes.

%I A252231 #13 Sep 06 2020 12:49:44
%S A252231 31,79,179,401,719,1619,3371,8819,12491,15671,23801,25919,28871,32801,
%T A252231 95219,118571,154871,161999,190121,266801,322571,364499,375371,449951,
%U A252231 524831,725801,772229,796001,820109,994571,1026029,1053401,1081121,1225109,1326089,1415039
%N A252231 Primes of the form (p+q)^2 + pq, where p and q are consecutive primes.
%H A252231 K. D. Bajpai, <a href="/A252231/b252231.txt">Table of n, a(n) for n = 1..12799</a>
%e A252231 79 is in the sequence because (3+5)^2 + 3*5 = 79, which is prime.
%e A252231 401 is in the sequence because (7+11)^2 + 7*11 = 401, which is prime.
%p A252231 count:= 0:
%p A252231 p:= 2:
%p A252231 while count < 100 do
%p A252231   q:= nextprime(p);
%p A252231   x:= (p+q)^2+p*q;
%p A252231   if isprime(x) then
%p A252231     count:= count+1;
%p A252231     a[count]:= x;
%p A252231   fi;
%p A252231   p:= q;
%p A252231 od:
%p A252231 seq(a[i],i=1..count); # _Robert Israel_, Dec 16 2014
%t A252231 Select[Table[(Prime[n] + Prime[n+1])^2 + Prime[n]Prime[n+1], {n,100}], PrimeQ[#] &]
%t A252231 Select[Total[#]^2+Times@@#&/@Partition[Prime[Range[100]],2,1],PrimeQ] (* _Harvey P. Dale_, Sep 06 2020 *)
%o A252231 (PARI) s=[]; for(k=1, 100, p=prime(k); q=prime(k+1); t=(p+q)^2 + p*q; if(isprime(t), s=concat(s, t))); s
%Y A252231 Cf. A000040, A007645, A003136, A243761, A252017.
%K A252231 nonn
%O A252231 1,1
%A A252231 _K. D. Bajpai_, Dec 15 2014