A140669 Numbers k such that (k+1)^(k+1) - k^k is prime.

1, 2, 3, 6, 10, 16, 105, 119, 1906, 7917

Offset: 1

Author

Rick L. Shepherd, May 21 2008

Keywords

• nonn
• hard
• more

Comments

Terms found with PrimeForm. Primes corresponding to 16, 105 and 119 certified with Primo. 7917 corresponds to a 30870-digit probable prime.

a(11) > 20000. - Michael S. Branicky, Apr 11 2025

Examples

			17^17 - 16^16 = 808793517812627212561, which is prime, so 16 is a term.
		

Links

• Eric Weisstein's World of Mathematics, Integer Sequence Primes
• Eric Weisstein's World of Mathematics, Power Difference Prime

Crossrefs

Cf. A134985. Equals A072164 - 1.

Programs

Mathematica

Select[Table[n,{n,8000}],PrimeQ[(#+1)^(#+1)-#^#]&] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2011 *)