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

1,1

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).

Links

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

Example

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

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 *)

Crossrefs

Cf. A007528.

Sequence in context: A238142 A190947 A203910 * A138762 A139777 A031633

Adjacent sequences: A354507 A354508 A354509 * A354511 A354512 A354513

Keyword

nonn

Author

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

Status

approved