A354510 Primes of the form p+q^2+r where p,q,r are three consecutive members of A007528.

13007, 28211, 36857, 39227, 86441, 272507, 345731, 459671, 467867, 553529, 599087, 746507, 777911, 788561, 910127, 1354901, 1425653, 1512923, 1587587, 1710869, 2039171, 2509061, 2624411, 3196913, 3617597, 3896657, 4161611, 4260077, 4359749, 4460549, 4536893, 4639757, 5171093, 5280791, 5673911, 5963351

Offset: 1

Author

J. M. Bergot and Robert Israel, Aug 16 2022

Keywords

• nonn

Comments

Primes of the form p+q^2+r where p, q and r are consecutive members of the sequence of primes of the form 6*k-1.

All terms == 5 (mod 6).

Examples

			a(3) = 36857 is in the sequence because 36857 = 179 + 191^2 + 197 and 179 = A007528(21), 191 = A007528(22) and 197 = A007528(23).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007528.

Programs

Maple

q:= 5: r:= 11: count:= 0: R:= NULL:
while count < 40 do
  p:= q; q:= r;
  do r:= r+6 until isprime(r);
  if isprime(p+q^2+r) then count:= count+1; R:= R, p+q^2+r fi
od:
R;

Mathematica

Select[#[[1]] + #[[2]]^2 + #[[3]] & /@ Partition[Select[Prime[Range[400]], Mod[#1, 6] == 5 &], 3, 1], PrimeQ] (* Amiram Eldar, Aug 16 2022 *)