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%I #23 Sep 08 2022 08:46:11
%S 1,2,4,16,52,80
%N Numbers n such that n^n - (n-1)^n + n is prime.
%C a(6) corresponds to a prime having 153 digits.
%C If it exists, a(7) > 5000.
%C n does not have the form 20k+2 (which leads to a multiple of 5) or 42k+26 (which leads to a multiple of 7).
%e 4 is in the sequence because 4^4 - 3^4 + 4 = 179 is prime.
%t Select[Range[1000], PrimeQ[#^# - (# - 1)^# + #] &]
%o (Magma) [n: n in [0..500] |IsPrime(n^n - (n-1)^n + n)];
%o (PARI) is(n)=ispseudoprime(n^n-(n-1)^n+n) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A085682.
%K nonn,more
%O 1,2
%A _Vincenzo Librandi_, Mar 13 2015
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