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Search: id:A157623
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| A157623 |
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a(n)=781250*n^2-455000*n+66249 (n>0) |
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+0
3
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| 392499, 2281249, 5732499, 10746249, 17322499, 25461249, 35162499, 46426249, 59252499, 73641249, 89592499, 107106249, 126182499, 146821249, 169022499, 192786249, 218112499, 245001249, 273452499, 303466249, 335042499, 368181249
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OFFSET
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1,1
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COMMENT
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If A=[A157621] 625*n.^2-364*n +53 (314, 1825, 4586, ,..,); Y=[A157622] 31250*n-9100 (22150, 53400, 84650..,); X=[A157623] 781250*n^2-455000*n+66249 (392499, 2281249, 5732499,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 392499^2-314*22150^2=1; 2281249^2-1825*53400^2=1; 5732499^2-4586*84650^2=1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=781250*n^2-455000*n+66249 (n>0)
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EXAMPLE
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For n=1, a(1)=392499; n=2, a(2)=2281249; n=3, a(3)=5732499
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CROSSREFS
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Sequence in context: A017456 A017588 A157741 this_sequence A145228 A131277 A050434
Adjacent sequences: A157620 A157621 A157622 this_sequence A157624 A157625 A157626
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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 03 2009
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