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A135791 Positive numbers of the form x^5-10x^3*y^2+5x*y^4 (where x,y are integers and x>y). 6
404, 1900, 3647, 5646, 12928, 13412, 14050, 27688, 30609, 36413, 45716, 51804, 60800, 74576, 90050, 98172 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A135792, union A135791 and A135792 see A135793. Squares of these numbers are of the form N^5-M^2 (where N belongs to A135787 and M to A057102) Proof uses: (x^5-10x^3 y^2+5xy^4)^2=(x^2+y^2)^5-(5x^4y-10x^2y^3+y^5)^2. [This line needs editing! - N. J. A. Sloane, Dec 04 2007]
Refers to A057102, which had an incorrect description and has been replaced by A256418.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
MATHEMATICA
a = {}; Do[Do[w = x^5 - 10x^3 y^2 + 5x y^4; If[w > 0 && w < 100000, AppendTo[a, w]], {x, y, 1000}], {y, 1, 1000}]; Union[a]
CROSSREFS
Sequence in context: A185640 A185637 A234675 * A187382 A306308 A185638
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 29 2007
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)