A161748 Smallest prime in the set of primes of the form x^n - y^(n-1), 1<=x, 1<=y.

2, 2, 2, 17, 31, 971, 127, 856073, 19427, 58537, 176123, 529393, 8191, 128467258961, 977123207545039, 43013953, 131071, 3814697134553, 524287, 79792266297087713

Offset: 1

Author

Cino Hilliard, Jun 17 2009

Keywords

• nonn

Comments

The function x^n -y^(n-1) has some prime values if x and y are covering the first quadrant. The smallest of these primes defines a(n).

Examples

			3^1 - 1^0 = 2, 2^2 - 2 = 2, 3^3 - 5^2 = 2, so 2,2,2 are the first 3 entries.
		

Programs

PARI

diffpowers(n,m) =
{
local(a,c=0,c2=0,j,k,y);
a=vector(floor(n^2/log(n^2)));
for(j=1,n,
for(k=1,n,
y=j^m-k^(m-1);
if(ispseudoprime(y), c++; a[c]=y;);
);
);
a=vecsort(a);
for(j=2,length(a),
if(a[j]!=a[j-1]&&a[j]!=0, c2++; print1(a[j]","); if(c2>100,break););
);
}

Extensions

Definition reworded - R. J. Mathar, Aug 30 2010