

A072164


Numbers k >= 1 such that f(k) = k^k  (k1)^(k1) is prime.


7




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  (k1)^(k1)); \\ Jinyuan Wang, Mar 19 2020


CROSSREFS

Cf. A007781 (n^n(n1)^(n1)). Equals A140669 + 1.
Sequence in context: A303025 A192669 A339484 * A060987 A006259 A119015
Adjacent sequences: A072161 A072162 A072163 * A072165 A072166 A072167


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



