A347075 Primes of the form p^3 + p^2 + p + 2 where p is prime.

41, 157, 401, 2381, 12721, 25261, 81401, 499361, 712981, 1455781, 2705081, 4357481, 7226501, 7684381, 7920401, 12061661, 12703861, 21330941, 22745561, 31955821, 49565921, 54583961, 59015581, 127517041, 237560441, 384769841, 455348741, 506897581, 570410861, 591294481, 866432341, 905167121

Offset

1,1

Comments

Except for 157, all terms == 1 (mod 20).

Links

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

Formula

a(n) = A164939(n)^3 + A164939(n)^2 + A164939(n) + 2.

Example

a(3) = 401 because 401 = 7^3 + 7^2 + 7 + 2 and 7 and 401 are prime.

Maple

f:= proc(p) local q;
if not isprime(p) then return NULL fi;
q:= p^3+p^2+p+2;
if isprime(q) then return q fi
end proc:
map(f, [seq(i, i=3..1000, 2)]);

Crossrefs

Cf. A164939.

Sequence in context: A221811 A105100 A141988 * A158602 A245743 A142839

Adjacent sequences: A347072 A347073 A347074 * A347076 A347077 A347078

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 15 2021

Status

approved