A279884 - OEIS

%I #9 Sep 08 2022 08:46:18

%S 2,17,4097,1679617,1000000000001,1283918464548865,

%T 4722366482869645213697,12748236216396078174437377,

%U 165251092644282265779977014214657,25986090120790645892257018950637850957185025,185302018885184100000000000000000000000000000001

%N a(n) = (prime(n)-1)^(prime(n)+1) + 1.

%C Prime terms are in A279883.

%C Subsequence of {A008788(n) + 1}.

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

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

%t Table[(# - 1)^(# + 1) + 1 &[Prime@ n], {n, 11}] (* _Michael De Vlieger_, Dec 23 2016 *)

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

%o (PARI) a(n) = (prime(n)-1)^(prime(n)+1)+1 \\ _Felix Fröhlich_, Dec 23 2016

%Y Cf. A000040, A279883.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Dec 23 2016