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Search: id:A157915
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| 650, 2525, 5650, 10025, 15650, 22525, 30650, 40025, 50650, 62525, 75650, 90025, 105650, 122525, 140650, 160025, 180650, 202525, 225650, 250025, 275650, 302525, 330650, 360025, 390650, 422525, 455650, 490025, 525650, 562525, 600650, 640025
(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
Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)=625*n^2+25 (n>0)
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EXAMPLE
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For n=1, a(1)=650; n=2, a(2)=2525; n=3, a(3)=5650
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CROSSREFS
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Cf. A005843, A157915
Sequence in context: A107551 A154358 A114047 this_sequence A158639 A162025 A035851
Adjacent sequences: A157912 A157913 A157914 this_sequence A157916 A157917 A157918
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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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