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
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
KEYWORD
hard,more,nonn
AUTHOR
Farideh Firoozbakht and M. F. Hasler, Nov 27 2009
STATUS
approved