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Search: id:A135794
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| A135794 |
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Numbers of the form x^5+10x^3*y^2+5x*y^4 (where x,y are integers). |
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+0
1
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| 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
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OFFSET
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1,1
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COMMENT
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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 (grafix(AT)csl.pl), Oct 10 2008]
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A000404, A050803, A057102, A135784, A060803, A135786, A135787, A135789, A135790, A135791, A135792, A135793, A135795, A135796.
Sequence in context: A027049 A060219 A014732 this_sequence A161851 A017030 A082921
Adjacent sequences: A135791 A135792 A135793 this_sequence A135795 A135796 A135797
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Nov 29 2007, Oct 10 2008
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