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Search: id:A157872
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| 6, 33, 78, 141, 222, 321, 438, 573, 726, 897, 1086, 1293, 1518, 1761, 2022, 2301, 2598, 2913, 3246, 3597, 3966, 4353, 4758, 5181, 5622, 6081, 6558, 7053, 7566, 8097, 8646, 9213, 9798, 10401, 11022, 11661, 12318, 12993, 13686, 14397, 15126, 15873, 16638
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OFFSET
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1,1
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COMMENT
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If A=[A157872] 9*n.^2-3 (6, 33, 78, 141,.,); Y=[A005843] 2*n (except the first term , 2,4,6,8,.,); X=[A140811] 6*n^2-1 (except the first term, 5,23,5395,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 5^2-6 *2^2=1; 23^2-33*4^2=1; 53^2-78*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=9*n^2-3 (n>0)
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EXAMPLE
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For n=1, a(1)=3; n=2, a(2)=33; n=3, a(3)=78
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CROSSREFS
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Cf. A005843, A140811
Sequence in context: A140521 A069065 A073343 this_sequence A153127 A135526 A057818
Adjacent sequences: A157869 A157870 A157871 this_sequence A157873 A157874 A157875
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009
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