A072164 Numbers k >= 1 such that f(k) = k^k - (k-1)^(k-1) is prime.

2, 3, 4, 7, 11, 17, 106, 120, 1907, 7918

Offset: 1

Author

Carlos Rivera, Jun 28 2002

Keywords

• nonn
• hard
• more

Comments

Enoch Haga proposed studying the primality of f(k) and he already knew the first 4 solutions. C. Rivera found the next four solutions using Ubasic and the last one using PRIMEFORM. Currently f(1907) is only a probable prime number, according to PRIMEFORM.

No other k < 25000. - T. D. Noe, Jun 12 2008

Examples

			2^2 - 1^1 = 3 is prime.
		

Links

• C. Rivera, Puzzle 185
• Eric Weisstein's World of Mathematics, Power Difference Prime
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A007781 (n^n-(n-1)^(n-1)). Equals A140669 + 1.

Programs

Mathematica

Select[Range[2, 200], PrimeQ[ #^#-(#-1)^(#-1)]&] (* T. D. Noe, Jun 12 2008 *)

PARI

isok(k) = ispseudoprime(k^k - (k-1)^(k-1)); \\ Jinyuan Wang, Mar 19 2020

Extensions

7918 found by Henri Lifchitz in 2001, contributed by Eric W. Weisstein, Nov 29 2005