A246060 Number of primes of the form k^(n - m) - m^k where n > 2 and positive k, m.
1, 1, 1, 5, 4, 5, 4, 7, 2, 8, 3, 10, 1, 12, 7, 13, 1, 11, 6, 13, 6, 19, 3, 12, 4, 17, 4, 10, 2, 18, 4, 15, 3, 21, 6, 14, 8, 18, 9, 23, 7, 9, 7, 21, 5, 13, 6, 22, 8, 16, 8, 24, 5, 22, 9, 12, 6, 26, 9, 26, 11, 27, 5, 30, 14, 34, 9, 23, 9, 48, 7, 11, 14, 37, 8, 32
Offset: 3
Keywords
Examples
a(3) = 1 because 2^(3 - 1) - 1^2 = 3 is prime with k = 2 and m = 1; a(4) = 1 because 2^(4 - 1) - 1^2 = 7 is prime with k = 2 and m = 1; a(5) = 1 because 3^(5 - 2) - 2^3 = 19 is prime with k = 3 and m = 2.
Programs
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PARI
a(n) = {my(k=2, q, v=List([])); if(ispseudoprime(q=2^(n-1)-1), listput(v, q)); while(k^(n-2)>2^k, if(ispseudoprime(q=k^(n-2)-2^k), listput(v, q)); k++); for(m=3, n-2, for(t=2, k-1, if(ispseudoprime(q=t^(n-m)-m^t), listput(v, q)))); #Set(v); } \\ Jinyuan Wang, Feb 24 2020
Extensions
Definition and a(7) corrected by Colin Barker, Sep 01 2014
More terms from Jinyuan Wang, Feb 24 2020