A181124 Difference of two positive 5th powers.

0, 31, 211, 242, 781, 992, 1023, 2101, 2882, 3093, 3124, 4651, 6752, 7533, 7744, 7775, 9031, 13682, 15783, 15961, 16564, 16775, 16806, 24992, 26281, 29643, 31744, 32525, 32736, 32767, 40951, 42242, 51273, 55924, 58025, 58806, 59017, 59048, 61051

Offset

1,2

Comments

Because x^5-y^5 = (x-y)(x^4+x^3*y+x^2*y^2+x*y^3+y^4), the difference of two 5th powers is a prime number only if x=y+1, in which case all the primes are in A121616. The number 7744 is the first of an infinite number of squares in this sequence.

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Mathematica

nn=10^9; p=5; Union[Reap[Do[n=i^p-j^p; If[n<=nn, Sow[n]], {i, Ceiling[(nn/p)^(1/(p-1))]}, {j, i}]][[2, 1]]]

Crossrefs

Cf. A024352 (squares), A181123 (cubes), A147857 (4th powers), A181125-A181128 (6th to 9th powers)

Sequence in context: A297758 A184058 A096906 * A142328 A022521 A152730

Adjacent sequences: A181121 A181122 A181123 * A181125 A181126 A181127

Keyword

nonn

Author

T. D. Noe, Oct 06 2010

Status

approved