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A072164 Numbers k >= 1 such that f(k) = k^k - (k-1)^(k-1) is prime. 7
2, 3, 4, 7, 11, 17, 106, 120, 1907, 7918 (list; graph; refs; listen; history; text; internal format)
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
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
CROSSREFS
Cf. A007781 (n^n-(n-1)^(n-1)). Equals A140669 + 1.
Sequence in context: A346020 A192669 A339484 * A060987 A359743 A006259
KEYWORD
nonn,hard,more
AUTHOR
Carlos Rivera, Jun 28 2002
EXTENSIONS
7918 found by Henri Lifchitz in 2001, contributed by Eric W. Weisstein, Nov 29 2005
STATUS
approved

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Last modified July 22 18:23 EDT 2024. Contains 374540 sequences. (Running on oeis4.)