

A241071


Numbers n such that k^n + (k1)^n + ... + 3^n + 2^n is prime for some k.


0




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.


LINKS



EXAMPLE

There exists a k such that k^2 + (k1)^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 + (k1)^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 + (k1)^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



STATUS

approved



