A240767 Numbers n such that n^k + (n-1)^k + ... + 3^k + 2^k is prime for some natural number k.

2, 3, 4, 7, 8, 11, 12, 16

Offset

1,1

Comments

a(9) > 19. See A240766 for more information.

a(n) is also the n-values such that A240766(n) is nonzero.

It is known that a(n) must be == 3 mod 4 or 0 mod 4 (except a(1) = 2) due to the parity of the sum. If an n-value is congruent to 1 mod 4 or 2 mod 4, the sum will always be even and thus, not prime.

It is known that 31, 36, 40, 43, 47, 56, 67, 83, and 171 are members of this sequence.

If n-1 is not squarefree, then n is not a member of this sequence.

Links

Table of n, a(n) for n=1..8.

Example

2^k is prime for at least one k (and only one k in this instance; k = 1). Thus, 2 is a member of this sequence.
3^k+2^k is prime for at least one k (see A082101). Thus, 3 is a member of this sequence.

Prog

(PARI) a(n)=for(k=1, 4000, if(ispseudoprime(sum(i=2, n, i^k)), return(k)))
n=1; while(n<200, if(a(n), print(a(n))); n+=1)

Crossrefs

Cf. A081507, A082101, A240766.

Sequence in context: A285506 A188190 A026808 * A342028 A368402 A284937

Adjacent sequences: A240764 A240765 A240766 * A240768 A240769 A240770

Keyword

nonn,hard,more

Author

Derek Orr, Apr 12 2014

Status

approved