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Search: id:A157916
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| 51, 201, 451, 801, 1251, 1801, 2451, 3201, 4051, 5001, 6051, 7201, 8451, 9801, 11251, 12801, 14451, 16201, 18051, 20001, 22051, 24201, 26451, 28801, 31251, 33801, 36451, 39201, 42051, 45001, 48051, 51201, 54451, 57801, 61251, 64801, 68451
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If A=[A157915] 625*n.^2+25 (650, 2525, 5650,.,); Y=[A005843] 2n (2,4,6,8, ,.,); X=[A157916] 50*n^2+ 1 (51, 201, 451..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 51^2-650 *2\^2=1; 201^2-2525*4^2=1; 451^2-5650*6^2=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)=50*n^2+1 (n>0)
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EXAMPLE
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For n=1, a(1)=51; n=2, a(2)=201; n=3, a(3)=451
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CROSSREFS
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Cf. A157915, A005843
Sequence in context: A069762 A031431 A157365 this_sequence A007264 A158640 A107253
Adjacent sequences: A157913 A157914 A157915 this_sequence A157917 A157918 A157919
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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 09 2009
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