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Search: id:A161735
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| A161735 |
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Distinct primes that are the difference between a fourth power and a cube. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For x=1 to 5000,y=1 to 5000, x^4 - y^3 = p two solutions for
primes p = 20393,3905513,5177033,28398833,10877895569. My guess is that the
number of duplicates is infinite.
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FORMULA
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If x^4-y^3 is prime for integers x,y list it.
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PROGRAM
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(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);
);
);
}
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CROSSREFS
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Sequence in context: A043194 A043974 A141972 this_sequence A142648 A002189 A002224
Adjacent sequences: A161732 A161733 A161734 this_sequence A161736 A161737 A161738
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KEYWORD
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nonn,uned
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Jun 17 2009
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