A264855 Integers n such that A002110(n)^2 - A002110(n) + 1 is prime.

1, 2, 4, 5, 10, 14, 15, 20, 23, 46, 96, 281, 367, 542, 1380, 1395

Offset

1,2

Comments

Initial primes of the form A002110(n)^2 - A002110(n) + 1 are 3, 31 and 43891.

Intersection of this sequence and A014545 gives the values of n such that A002110(n)^3 + 1 is semiprime.

Links

Table of n, a(n) for n=1..16.

Example

a(1) = 1 because 2^2 - 2 + 1 = 3 is prime.
a(2) = 2 because 6^2 - 6 + 1 = 31 is prime.
a(3) = 4 because 210^2 - 210 + 1 = 43891 is prime.

Mathematica

Select[Range@ 400, PrimeQ[#^2 - # + 1 &@ Product[Prime@ k, {k, #}]] &] (* Michael De Vlieger, Nov 28 2015 *)

Prog

(PARI) a002110(n) = prod(k=1, n, prime(k));
for(n=0, 1e3, if(ispseudoprime(a002110(n)^2 - a002110(n) + 1), print1(n, ", ")))

Crossrefs

Cf. A002110, A014545, A092061.

Sequence in context: A018360 A133585 A218936 * A154318 A008283 A002237

Adjacent sequences: A264852 A264853 A264854 * A264856 A264857 A264858

Keyword

nonn,more

Author

Altug Alkan, Nov 26 2015

Status

approved