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

17, 73, 113, 131, 229, 409, 443, 617, 673, 739, 953, 1153, 1171, 1889, 2393, 5087, 6217, 6553, 8669, 9433, 9973, 11321, 11897, 13877, 14633, 14737, 15823, 17377, 18539, 19081, 19441, 20393, 20611, 21841, 25469, 26249, 26833, 28649, 29599

Offset

1,1

Comments

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.

My guess is that the number of duplicates is infinite.

Links

Table of n, a(n) for n=1..39.

Formula

If x^4-y^3 is prime for integers x >=1, y>=1, list it.

Prog

(PARI) difffourthcube(n) =
{
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^4-k^3;
if(ispseudoprime(y),
c++;
\\ print(j", "k", "y);
a[c]=y;
);
);
);
a=vecsort(a);
for(j=2, c,
if(a[j]!=a[j-1]&&a[j]!=0,
c2++;
print1(a[j]", ");
if(c2>100, break);
);
);
}

Crossrefs

Sequence in context: A043194 A043974 A141972 * A142648 A002189 A002224

Adjacent sequences: A161732 A161733 A161734 * A161736 A161737 A161738

Keyword

nonn

Author

Cino Hilliard, Jun 17 2009

Status

approved