OFFSET
1,2
COMMENTS
It is known that a(n) is even for all n (except a(1)). See A241070 for more restrictions on a(n).
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.
EXAMPLE
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.
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.
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.
PROG
(PARI) a(n)=for(k=1, 7500, if(ispseudoprime(sum(i=2, k, i^n)), return(k)))
n=1; while(n<250, if(a(n), print(n)); n+=1)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Derek Orr, Apr 15 2014
STATUS
approved