A279884 a(n) = (prime(n)-1)^(prime(n)+1) + 1.

2, 17, 4097, 1679617, 1000000000001, 1283918464548865, 4722366482869645213697, 12748236216396078174437377, 165251092644282265779977014214657, 25986090120790645892257018950637850957185025, 185302018885184100000000000000000000000000000001

Offset: 1

Author

Jaroslav Krizek, Dec 23 2016

Keywords

• nonn

Comments

Prime terms are in A279883.

Subsequence of {A008788(n) + 1}.

Conjecture: If (n-1)^(n+1) + 1 is a prime, then n = prime.

Examples

			For n=3; a(3) = (prime(3)-1)^(prime(3)+1) + 1 = 4^6 + 1 = 4097.
		

Crossrefs

Cf. A000040, A279883.

Programs

Magma

[(NthPrime(n)-1)^(NthPrime(n)+1)+1: n in[1..50]]

Mathematica

Table[(# - 1)^(# + 1) + 1 &[Prime@ n], {n, 11}] (* Michael De Vlieger, Dec 23 2016 *)

PARI

a(n) = (prime(n)-1)^(prime(n)+1)+1 \\ Felix Fröhlich, Dec 23 2016