A356003 Primes p such that p = 3*a + 1 with p + a*a*(a+1) prime or p = 3*a + 2 with p + a*(a+1)*(a+1) prime.

2, 7, 11, 17, 19, 29, 61, 89, 97, 127, 179, 251, 263, 269, 277, 307, 331, 397, 433, 439, 457, 467, 479, 523, 569, 601, 647, 739, 773, 809, 863, 883, 937, 953, 971, 1063, 1087, 1091, 1171, 1181, 1307, 1447, 1483, 1511, 1583, 1621, 1657, 1663, 1783, 1789, 1801, 1811, 1879, 1889, 1933, 1951, 1987

Offset

1,1

Comments

Primes p that can be divided in three parts differing by at most 1 with p + the product of the parts prime.

Links

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

Example

a(3) = 11 is a term because 11 = 3+4+4 with 11+3*4*4 = 59 prime.

Maple

filter:= proc(p) local a, t;
   if not isprime(p) then return false fi;
   if p mod 3 = 1 then a:= (p-1)/3; t:= p+a^2*(a+1) else a:= (p-2)/3; t:= p+a*(a+1)^2 fi;
   isprime(t)
end proc:
select(filter, [2, seq(i, i=5..2000, 2)]);

Mathematica

q[p_] := Module[{r = Mod[p, 3], a}, a = (p-r)/3; r > 0 && PrimeQ[p+a*(a+1)*(a+r-1)]]; Select[Prime[Range[300]], q] (* Amiram Eldar, Jul 22 2022 *)

Crossrefs

Sequence in context: A243009 A155009 A045371 * A063205 A090613 A063097

Adjacent sequences: A356000 A356001 A356002 * A356004 A356005 A356006

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 22 2022

Status

approved