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%I #14 Apr 11 2025 16:47:51
%S 1,2,3,6,10,16,105,119,1906,7917
%N Numbers k such that (k+1)^(k+1) - k^k is prime.
%C Terms found with PrimeForm. Primes corresponding to 16, 105 and 119 certified with Primo. 7917 corresponds to a 30870-digit probable prime.
%C a(11) > 20000. - _Michael S. Branicky_, Apr 11 2025
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerDifferencePrime.html">Power Difference Prime</a>
%e 17^17 - 16^16 = 808793517812627212561, which is prime, so 16 is a term.
%t Select[Table[n,{n,8000}],PrimeQ[(#+1)^(#+1)-#^#]&] (* _Vladimir Joseph Stephan Orlovsky_, Mar 03 2011 *)
%Y Cf. A134985. Equals A072164 - 1.
%K nonn,hard,more
%O 1,2
%A _Rick L. Shepherd_, May 21 2008