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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A139855 A139901 A242777 * A044169 A044550 A055810

Adjacent sequences: A252228 A252229 A252230 * A252232 A252233 A252234

Keyword

nonn

Author

K. D. Bajpai, Dec 15 2014

Status

approved