cp's OEIS Frontend

A161735 Primes that are the difference between a fourth power and a positive cube.

%I A161735 #5 Oct 01 2013 21:35:30
%S A161735 17,73,113,131,229,409,443,617,673,739,953,1153,1171,1889,2393,5087,
%T A161735 6217,6553,8669,9433,9973,11321,11897,13877,14633,14737,15823,17377,
%U A161735 18539,19081,19441,20393,20611,21841,25469,26249,26833,28649,29599
%N A161735 Primes that are the difference between a fourth power and a positive cube.
%C A161735 There are primes like p = 20393, 3905513, 5177033, 28398833, or 10877895569 which have more than one representation p=x^4-y^3, with x,y>=1.
%C A161735 My guess is that the number of duplicates is infinite.
%F A161735 If x^4-y^3 is prime for integers x >=1, y>=1, list it.
%o A161735 (PARI) difffourthcube(n) =
%o A161735 {
%o A161735 local(a,c=0,c2=0,j,k,y);
%o A161735 a=vector(floor(n^2/log(n^2)));
%o A161735 for(j=1,n,
%o A161735 for(k=1,n,
%o A161735 y=j^4-k^3;
%o A161735 if(ispseudoprime(y),
%o A161735 c++;
%o A161735 \\ print(j","k","y);
%o A161735 a[c]=y;
%o A161735 );
%o A161735 );
%o A161735 );
%o A161735 a=vecsort(a);
%o A161735 for(j=2,c,
%o A161735 if(a[j]!=a[j-1]&&a[j]!=0,
%o A161735 c2++;
%o A161735 print1(a[j]",");
%o A161735 if(c2>100,break);
%o A161735 );
%o A161735 );
%o A161735 }
%K A161735 nonn
%O A161735 1,1
%A A161735 _Cino Hilliard_, Jun 17 2009