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

3,4

Links

Table of n, a(n) for n=3..78.

Example

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.

Prog

(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

Crossrefs

Cf. A242113, A245459.

Sequence in context: A093348 A262604 A276500 * A316327 A001050 A113784

Adjacent sequences: A246057 A246058 A246059 * A246061 A246062 A246063

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 23 2014

Extensions

Definition and a(7) corrected by Colin Barker, Sep 01 2014

More terms from Jinyuan Wang, Feb 24 2020

Status

approved