A263925 a(n) = least m > 1 such that m + (prime(n)#)^n is prime.

3, 5, 11, 19, 89, 323, 29, 61, 79, 199, 563, 181, 353, 1307, 257, 709, 1237, 1277, 1609, 1237, 4157, 2017, 577, 157, 191, 1063, 239, 823, 1607, 4159, 139, 11527, 2339, 18457, 4079, 463, 1861, 1123, 8699, 16561, 719, 4327, 9311, 1693, 3067, 4243, 22397, 4079, 3989, 24071

Offset: 1

Author

Alexei Kourbatov, Oct 30 2015

Keywords

• nonn

Comments

Here prime(n)# denotes the primorial A002110(n), i.e., the product of the first n primes. Terms a(n) are often (but not always) prime; out of the first fifty terms, only one (a(6)=323) is composite.

The definition is similar to Fortunate numbers (A005235); however, in A005235 the primorial is not raised to the n-th power. Unlike this sequence, all known Fortunate numbers are prime.

Examples

			(prime(2)#)^2=36. a(2)=5 because 5 is the minimal m>1 such that m+36 is prime.
		

Crossrefs

Cf. A002110, A005235, A181555, A264050.

Programs

Mathematica

Table[m = 2; While[! PrimeQ[m + Product[Prime@ i, {i, n}]^n], m++]; m, {n, 30}] (* Michael De Vlieger, Nov 11 2015 *)

PARI

a(n)=my(s=prod(i=1,n,prime(i))^n); nextprime(s+2)-s