cp's OEIS Frontend

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

%I A161748 #7 Oct 01 2013 21:35:30
%S A161748 2,2,2,17,31,971,127,856073,19427,58537,176123,529393,8191,
%T A161748 128467258961,977123207545039,43013953,131071,3814697134553,524287,
%U A161748 79792266297087713
%N A161748 Smallest prime in the set of primes of the form x^n - y^(n-1), 1<=x, 1<=y.
%C A161748 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).
%e A161748 3^1 - 1^0 = 2, 2^2 - 2 = 2, 3^3 - 5^2 = 2, so 2,2,2 are the first 3 entries.
%o A161748 (PARI) diffpowers(n,m) =
%o A161748 {
%o A161748 local(a,c=0,c2=0,j,k,y);
%o A161748 a=vector(floor(n^2/log(n^2)));
%o A161748 for(j=1,n,
%o A161748 for(k=1,n,
%o A161748 y=j^m-k^(m-1);
%o A161748 if(ispseudoprime(y), c++; a[c]=y;);
%o A161748 );
%o A161748 );
%o A161748 a=vecsort(a);
%o A161748 for(j=2,length(a),
%o A161748 if(a[j]!=a[j-1]&&a[j]!=0, c2++; print1(a[j]","); if(c2>100,break););
%o A161748 );
%o A161748 }
%K A161748 nonn
%O A161748 1,1
%A A161748 _Cino Hilliard_, Jun 17 2009
%E A161748 Definition reworded - _R. J. Mathar_, Aug 30 2010