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%I #18 Sep 08 2022 08:45:53
%S 7,79,1021,3486784393,155568095557812211,
%T 6176733962839469999999999999999999999999999971
%N Primes in A014293.
%C Prime solutions to the classical "Monkey and Coconut Problem." Primes of the form n^(n+1)-n+1. A014293(n) is prime for n = 2, 3, 4, 9, 14, 30, 62, 75, 156, ..., .
%C The next term has 113 digits.
%F {n^(n+1)-n+1 : n nonnegative integer and n^(n+1)-n+1 in A000040} == A014293 INTERSECTION A000040.
%e A014293(0) = A014293(1) = 1 is nonprime, so 1 is not in this sequence.
%e A014293(2) = 7 is prime, so 7 is in this sequence.
%e A014293(3) = 79 is prime, so 79 is in this sequence.
%e A014293(4) = 1021 is prime, so 1021 is in this sequence.
%e A014293(5) = 15621 = 3 * 41 * 127 is nonprime, so 15621 is not in this sequence.
%t Select[#^(# + 1) - # + 1 & /@ Range@ 75, PrimeQ]
%o (Magma) [ a: n in [0..250] | IsPrime(a) where a is (n^(n+1)-n+1)] // _Vincenzo Librandi_, Jan 30 2011
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Dec 07 2010
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