A072164 - OEIS

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

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OFFSET

1,1

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

LINKS

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

C. Rivera, Puzzle 185

Eric Weisstein's World of Mathematics, Power Difference Prime

Eric Weisstein's World of Mathematics, Integer Sequence Primes

EXAMPLE

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

MATHEMATICA

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

PROG

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