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Search: id:A001093
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| 0, 1, 2, 9, 28, 65, 126, 217, 344, 513, 730, 1001, 1332, 1729, 2198, 2745, 3376, 4097, 4914, 5833, 6860, 8001, 9262, 10649, 12168, 13825, 15626, 17577, 19684, 21953, 24390, 27001, 29792, 32769, 35938, 39305, 42876, 46657, 50654, 54873, 59320
(list; graph; listen)
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OFFSET
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-1,3
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COMMENT
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Sequence allows us to find X values of the equation: 1!*X^4 + 2!*(X - 1)^3 + 3!*(X - 2)^2 + (4^2)*(X -3) + 5^2 = Y^3. To prove that X = n^3 + 1: Y^3 = 1!*X^4 + 2!*(X - 1)^3 + 3!*(X - 2)^2 + (4^2)*(X -3) + 5^2 = X^4 + 2*(X - 1)^3 + 6*(X - 2)^2 + 16(X -3) + 25 = X^4 + 2*X^3 - 2X - 1 = (X - 1)(X^3 + 3*X^2 + 3X + 1) = (X - 1)*(X + 1)^3 it means: (X - 1) must be a cube, so X = n^3 + 1 and Y = n(n^3 + 2). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 04 2007
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CROSSREFS
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Sequence in context: A115186 A090900 A100293 this_sequence A121643 A131066 A058877
Adjacent sequences: A001090 A001091 A001092 this_sequence A001094 A001095 A001096
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KEYWORD
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nonn
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AUTHOR
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njas, Ray Wills [ rwills(AT)vmprofs.estec.esa.nl ]
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000
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