A135794 Numbers of the form x^5 + 10*x^3*y^2 + 5*x*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

Author

Artur Jasinski, Nov 29 2007, Oct 10 2008

Keywords

• nonn

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 ((y + x)^5 - (y - x)^5)/2 = x^5 + 10*x^3*y^2 + 5*x*y^4. - 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Refers to A057102, which had an incorrect description and has been replaced by A256418.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

Crossrefs

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

Programs

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]