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

31, 79, 179, 401, 719, 1619, 3371, 8819, 12491, 15671, 23801, 25919, 28871, 32801, 95219, 118571, 154871, 161999, 190121, 266801, 322571, 364499, 375371, 449951, 524831, 725801, 772229, 796001, 820109, 994571, 1026029, 1053401, 1081121, 1225109, 1326089, 1415039

Offset: 1

Author

K. D. Bajpai, Dec 15 2014

Keywords

• nonn

Examples

			79 is in the sequence because (3+5)^2 + 3*5 = 79, which is prime.
401 is in the sequence because (7+11)^2 + 7*11 = 401, which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..12799

Crossrefs

Cf. A000040, A007645, A003136, A243761, A252017.

Programs

Maple

count:= 0:
p:= 2:
while count < 100 do
  q:= nextprime(p);
  x:= (p+q)^2+p*q;
  if isprime(x) then
    count:= count+1;
    a[count]:= x;
  fi;
  p:= q;
od:
seq(a[i],i=1..count); # Robert Israel, Dec 16 2014

Mathematica

Select[Table[(Prime[n] + Prime[n+1])^2 + Prime[n]Prime[n+1], {n,100}], PrimeQ[#] &]
Select[Total[#]^2+Times@@#&/@Partition[Prime[Range[100]],2,1],PrimeQ] (* Harvey P. Dale, Sep 06 2020 *)

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