login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

CROSSREFS

Cf. A007781 (n^n-(n-1)^(n-1)). 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 15 12:25 EDT 2021. Contains 343916 sequences. (Running on oeis4.)