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 A166853 a(n) is the smallest number m such that m^m-n is prime, or zero if there is no such m. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence with the unknown terms a(n) indicated by -n: (0's occur for n=9, 49, 81, 121....) 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, -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, 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, 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, 22,5,-103,-104,4,5,4,11,12,39,-111,... 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. If it exists, a(26) > 25000. - Robert Price, Apr 26 2019 LINKS FORMULA a(n)=0 if n=3^2 or n=(2k+1)^2 > 25, or n = (6k+1)^3 = A016923(k) with k>0. EXAMPLE We have a(1)=2 since 1^1-1 is not prime, but 2^2-1 is prime. 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. 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,.... a(115)=2736 is the largest known term. 2736^2736-115 is a probable prime. CROSSREFS Cf. A087037, A087038, A016754, A016923, A100407, A100408, A166852. Sequence in context: A021442 A296851 A331750 * A143440 A093731 A195361 Adjacent sequences:  A166850 A166851 A166852 * A166854 A166855 A166856 KEYWORD hard,more,nonn AUTHOR Farideh Firoozbakht and M. F. Hasler, Nov 27 2009 STATUS approved

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)