A241071 Numbers n such that k^n + (k-1)^n + ... + 3^n + 2^n is prime for some k.

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

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

Table of n, a(n) for n=1..7.

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

Sequence in context: A334614 A185449 A096922 * A353026 A356431 A345444

Adjacent sequences: A241068 A241069 A241070 * A241072 A241073 A241074

Keyword

nonn,hard,more

Author

Derek Orr, Apr 15 2014

Status

approved