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

2,1

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.)

Links

Table of n, a(n) for n=2..50.

Example

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

Prog

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

Crossrefs

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

Sequence in context: A075409 A258655 A174362 * A058079 A076787 A332763

Adjacent sequences: A268605 A268606 A268607 * A268609 A268610 A268611

Keyword

nonn

Author

Alexei Kourbatov, Feb 08 2016

Status

approved