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A264855
Integers n such that A002110(n)^2 - A002110(n) + 1 is prime.
0
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.
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
KEYWORD
nonn,more
AUTHOR
Altug Alkan, Nov 26 2015
STATUS
approved