A135794 Numbers of the form x^5+10x^3*y^2+5x*y^4 (where x,y are integers).

16, 121, 122, 496, 512, 528, 1441, 1562, 1563, 1684, 3376, 3872, 3888, 3904, 4400, 6841, 8282, 8403, 8404, 8525, 9966, 12496, 15872, 16368, 16384, 16400, 16896, 20272, 21121, 27962, 29403, 29524, 29525, 29646, 31087, 33616, 37928, 46112

Offset

1,1

Comments

Squares of these numbers are of the form N^5+M^2 (where N belongs to A000404 and M to A135795) Proof uses: (x^5+10x^3 y^2+5xy^4)^2=(x^2-y^2)^5+(5x^4y+10x^2y^3+y^5)^2

Also numbers of the form ((x + y)^5 - (x - y)^5))/2 = x^5 + 10x^3*y^2 + 5x*y^4 [From Artur Jasinski, Oct 10 2008]

Refers to A057102, which had an incorrect description and has been replaced by A256418. As a result the present sequence should be re-checked. - N. J. A. Sloane, Apr 06 2015

Links

Table of n, a(n) for n=1..38.

Mathematica

a = {}; Do[Do[w = x^5 + 10x^3 y^2 + 5x y^4; If[w < 100000, AppendTo[a, w]], {x, 1, 1000}], {y, 1, 1000}]; Union[a]

Crossrefs

Cf. A000404, A050803, A057102, A135784, A060803, A135786, A135787, A135789, A135790, A135791, A135792, A135793, A135795, A135796.

Sequence in context: A185760 A301649 A014732 * A161851 A171584 A017030

Adjacent sequences: A135791 A135792 A135793 * A135795 A135796 A135797

Keyword

nonn

Author

Artur Jasinski, Nov 29 2007, Oct 10 2008

Status

approved