A241071 - OEIS

%I #27 May 17 2014 03:03:04

%S 1,2,4,6,8,10,12

%N Numbers n such that k^n + (k-1)^n + ... + 3^n + 2^n is prime for some k.

%C It is known that a(n) is even for all n (except a(1)). See A241070 for more restrictions on a(n).

%C It is known that 16, 24, 32, 36, 42, 48, 56, 60, 66, 72, 80, 108, 110, 120, 144, and 192 are all members of this sequence.

%e There exists a k such that k^2 + (k-1)^2 + ... + 3^2 + 2^2 is prime (let k = 3). Thus, 2 is a member of this sequence.

%e There exists a k such that k^4 + (k-1)^4 + ... + 3^4 + 2^4 is prime (let k = 3). Thus, 4 is a member of this sequence.

%e However, there does not exist a k such that k^3 + (k-1)^3 + ... + 3^3 + 2^3 is prime (this is tested for k < 7500). Thus, 3 is not a member of this sequence.

%o (PARI) a(n)=for(k=1,7500,if(ispseudoprime(sum(i=2,k,i^n)),return(k)))

%o n=1;while(n<250,if(a(n),print(n));n+=1)

%K nonn,hard,more

%O 1,2

%A _Derek Orr_, Apr 15 2014