1,1

For even n > 4 = 2m, x^2m - y^(2m-2) = (x^m)^2 - y^((m-1))^2 is divisible by

x^m - y^(m-1) which is not prime. This accounts for the phrase "if they exist"

in the definition.

(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++;

\\ print(j", "k", "y);

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);

);

);

}

Sequence in context: A155046 A033318 A093780 this_sequence A101307 A096899 A154448

Adjacent sequences: A161746 A161747 A161748 this_sequence A161750 A161751 A161752

nonn,uned

Cino Hilliard (hillcino368(AT)hotmail.com), Jun 17 2009