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Search: id:A157740
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| 18564, 37086, 55608, 74130, 92652, 111174, 129696, 148218, 166740, 185262, 203784, 222306, 240828, 259350, 277872, 296394, 314916, 333438, 351960, 370482, 389004, 407526, 426048, 444570, 463092, 481614, 500136, 518658, 537180, 555702
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OFFSET
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1,1
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COMMENT
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If A=[A031699] 441*n.^2+2*n (443, 1768, 3975,..,); Y=[A157740] 18522*n+ 42 (18564, 37086, 55608..,); X=[A157741] 388962*n^2+1764*n +1 (390727, 1559377, 3505951,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 390727^2-443 *18564^2=1; 1559377^2-1768*37086^2=1; 3505951^2-3975*55608^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Philippe Chevanne, Pell Equation
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FORMULA
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a(n)=18522*n+42 (n>0)
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EXAMPLE
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For n=1, a(1)=18564; n=2, a(2)=37086; n=3, a(3)=55608
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CROSSREFS
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Cf. A031699, A157741
Sequence in context: A035924 A157738 A031817 this_sequence A081416 A051795 A089522
Adjacent sequences: A157737 A157738 A157739 this_sequence A157741 A157742 A157743
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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 05 2009
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