%I #13 Nov 28 2015 19:16:45
%S 1,2,4,5,10,14,15,20,23,46,96,281,367,542,1380,1395
%N Integers n such that A002110(n)^2 - A002110(n) + 1 is prime.
%C Initial primes of the form A002110(n)^2 - A002110(n) + 1 are 3, 31 and 43891.
%C Intersection of this sequence and A014545 gives the values of n such that A002110(n)^3 + 1 is semiprime.
%e a(1) = 1 because 2^2 - 2 + 1 = 3 is prime.
%e a(2) = 2 because 6^2 - 6 + 1 = 31 is prime.
%e a(3) = 4 because 210^2 - 210 + 1 = 43891 is prime.
%t Select[Range@ 400, PrimeQ[#^2 - # + 1 &@ Product[Prime@ k, {k, #}]] &] (* _Michael De Vlieger_, Nov 28 2015 *)
%o (PARI) a002110(n) = prod(k=1, n, prime(k));
%o for(n=0, 1e3, if(ispseudoprime(a002110(n)^2 - a002110(n) + 1), print1(n, ", ")))
%Y Cf. A002110, A014545, A092061.
%K nonn,more
%O 1,2
%A _Altug Alkan_, Nov 26 2015
|