Search: id:A072164
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%I A072164
%S A072164 2,3,4,7,11,17,106,120,1907,7918
%N A072164 Numbers n (>= 1) such that f(n) = n^n - (n-1)^(n-1) is prime.
%C A072164 Enoch Haga proposed studying the primality of f(n) 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.
%C A072164 No other n<25000. - T. D. Noe (noe(AT)sspectra.com), Jun 12 2008
%H A072164 C. Rivera, <a href="http://www.primepuzzles.net">Puzzle 185</a>
%H A072164 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PowerDifferencePrime.html">Power Difference Prime</a>
%H A072164 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               IntegerSequencePrimes.html">Integer Sequence Primes</a>
%e A072164 2^2 - 1^1 = 3 = prime
%t A072164 Select[Range[2, 200], PrimeQ[ #^#-(#-1)^(#-1)]&] (T. D. Noe)
%Y A072164 Cf. A007781 (n^n-(n-1)^(n-1)). Equals A140669 + 1.
%Y A072164 Sequence in context: A165407 A039897 A050193 this_sequence A060987 A006259 
               A119015
%Y A072164 Adjacent sequences: A072161 A072162 A072163 this_sequence A072165 A072166 
               A072167
%K A072164 hard,nonn
%O A072164 1,1
%A A072164 Carlos B. Rivera F. (crivera(AT)primepuzzles.net), Jun 28 2002
%E A072164 7918 found by Henri Lifchitz in 2001, contributed by Eric Weisstein (eric(AT)weisstein.com), 
               Nov 29, 2005

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