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%I #9 Apr 26 2019 10:42:40
%S 2,2,8,3,4,5,6,3,0,3,78,13,6,3,4,3,4,17,12,3,118,3,4,3,3
%N a(n) is the smallest number m such that m^m-n is prime, or zero if there is no such m.
%C The sequence with the unknown terms a(n) indicated by -n:
%C (0's occur for n=9, 49, 81, 121....)
%C 2,2,8,3,4,5,6,3,0,3,78,13,6,3,4,3,4,17,12,3,118,3,4,3,3,
%C -26,4,-28,4,487,90,9,4,-34,24,5,6,271,28,969,-41,5,-43,7,4,5,32,37,0,621,
%C 20,15,34,7,6,9,4,5,4,7,-61,7,4,5,4,-66,6,63,134,27,10,35,102,31,4,
%C 5,4,569,-79,13,0,15,4,5,-85,7,110,5,4,131,1122,7,4,11,8,7,6,9,4,-100,
%C 22,5,-103,-104,4,5,4,11,12,39,-111,...
%C If they exist, the first two unknown terms, a(26) and a(28), they are greater than 10000. All other unknown terms a(n), for n<112 are greater than 4000.
%C If it exists, a(26) > 25000. - _Robert Price_, Apr 26 2019
%F a(n)=0 if n=3^2 or n=(2k+1)^2 > 25, or n = (6k+1)^3 = A016923(k) with k>0.
%e We have a(1)=2 since 1^1-1 is not prime, but 2^2-1 is prime.
%e a(9)=0 since 2^2-9 is not prime, and if m is an even number greater than 2 then m^m-9=(m^(m/2)-3)*(m^(m/2)+3) is composite. So there is no number m such that m^m-9 is prime. The same applies to any odd square > 25.
%e We have a(25)=3 since 3^3-25=2 is prime. But 25 is the only known square of the form m^m-2, so a(n)=0 for other odd squares > 25, e.g., n = 49,81,121,....
%e a(115)=2736 is the largest known term. 2736^2736-115 is a probable prime.
%Y Cf. A087037, A087038, A016754, A016923, A100407, A100408, A166852.
%K hard,more,nonn
%O 1,1
%A _Farideh Firoozbakht_ and _M. F. Hasler_, Nov 27 2009
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