A295741 a(n) is smallest divisor d of the n-th primorial such that d + prime(n)#/d is prime.

1, 1, 1, 1, 1, 1, 2, 5, 6, 10, 2, 1, 2, 11, 7, 2, 41, 2, 5, 5, 5, 3, 51, 10, 3, 14, 37, 10, 7, 2, 17, 17, 62, 21, 3, 38, 17, 47, 13, 17, 13, 7, 21, 83, 10, 138, 10, 26, 2, 7, 19, 31, 15, 13, 5, 23, 103, 19, 5, 95, 61, 6, 15, 2, 35, 13, 19, 65, 39, 7, 43, 73, 13, 26, 97, 1, 91, 2, 78, 19, 39, 34, 167, 82, 10, 38, 66, 58, 2, 46, 71

Offset: 0

Author

Thomas Ordowski and Robert G. Wilson v, Nov 26 2017

Keywords

• nonn

Comments

Conjecture: a(n) < prime(n)^2 for n > 0.

a(n) = 1 iff n belongs to A014545.

Inspired by A293756.

Examples

			a(3) = 1 because 1 + prime(3)#/1 = 1 + 2*3*5 = 31 and 31 is a prime;
a(6) = 2 because 2 + prime(6)#/2 = 2 + 2*3*5*7*11*13/2 = 15017 and that is a prime;
a(7) = 5 because 5 + prime(7)#/5 = 5 + 2*3*5*7*11*13*17/5 = 102107 which is a prime; etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002110, A005235, A014545.

Programs

Mathematica

f[n_] := Block[{d = 1, p = Fold[Times, 1, Prime@ Range@ n]}, While[ !PrimeQ[d + p/d], d++]; d]; Array[f, 90]

PARI

a(n)=my(P=vecprod(primes(n))); for(d=1,P, if(P%d==0 && ispseudoprime(d+P/d), return(d))) \\ Charles R Greathouse IV, Nov 27 2017