A268608 a(n) is the least m > 1 such that (prime(n)#)^n - m is prime.

5, 7, 19, 23, 41, 163, 67, 257, 83, 109, 43, 359, 293, 647, 277, 1567, 983, 419, 1723, 83, 103, 3089, 719, 733, 1723, 457, 331, 2729, 3389, 1123, 863, 1123, 1871, 6211, 19717, 5323, 5749, 419, 887, 811, 617, 2851, 2531, 5023, 6883, 6661, 2879, 16433, 19471

Offset: 2

Author

Alexei Kourbatov, Feb 08 2016

Keywords

• nonn

Comments

Here prime(n)# denotes the primorial A002110(n), i.e., the product of the first n primes. a(1) is not defined (there are no primes less than 2).

The definition is similar to Lesser Fortunate numbers (A055211) - but here primorials A002110(n) are raised to the n-th power.

Similar to Fortunate numbers (A005235) and Lesser Fortunate numbers (A055211), the first fifty terms are all prime. (Cf. A263925 where the 6th term is composite.)

Examples

			a(2)=5 because m=5 is the least m > 1 such that A002110(2)^2 - m is prime.
		

Crossrefs

Cf. A002110, A005235, A055211, A264050, A263925, A268607.

Programs

PARI

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