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

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

Offset

1,2

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

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Eric Weisstein's World of Mathematics, Power Difference Prime

Example

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

Mathematica

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

Crossrefs

Cf. A134985. Equals A072164 - 1.

Sequence in context: A294444 A066895 A105075 * A001636 A347786 A036588

Adjacent sequences: A140666 A140667 A140668 * A140670 A140671 A140672

Keyword

nonn,hard,more

Author

Rick L. Shepherd, May 21 2008

Status

approved