A240748 Numbers n such that n^k - (n-1)^k - ... - 3^k - 2^k - 1 is prime for some k.

2, 4, 5, 6, 10, 13

Offset: 1

Author

Derek Orr, Apr 11 2014

Keywords

• nonn
• more
• hard

Comments

a(7) > 13. See A240747 for more information.

a(n) is also the n-values such that A240747(n) is nonzero.

It is known that a(n) == 1 mod 4 or 2 mod 4 (except a(2) = 4).

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

It is known that 17, 22, 30, 41, 66, and 194 are members of this sequence.

Examples

			There are primes of the form 2^k-1 (A000043) so 2 is a member of this sequence.
		

Crossrefs

Cf. A000043, A240747, A240507, A240503.

Programs

PARI

s(n) = for(k=1,6000,if(ispseudoprime(n^k-sum(i=1,n-1,i^k)),return(k)))
n=1; while(n<200,if(s(n),print(n));n+=1)