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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)