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Search: id:A157919
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| 49, 199, 449, 799, 1249, 1799, 2449, 3199, 4049, 4999, 6049, 7199, 8449, 9799, 11249, 12799, 14449, 16199, 18049, 19999, 22049, 24199, 26449, 28799, 31249, 33799, 36449, 39199, 42049, 44999, 48049, 51199, 54449, 57799, 61249, 64799, 68449
(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=[A157918] 625*n.^2-25 (600, 2475, 5600,.,); Y=[A005843] 2n (2,4,6,8, ,.,); X=[A157919] 50*n^2- 1 (49, 199, 449.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 49^2-600 *2\^2=1; 199^2-2475*4^2=1; 449^2-5600*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)=50*n^2-1 (n>0)
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EXAMPLE
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For n=1, a(1)=49; n=2, a(2)=199; n=3, a(3)=449
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CROSSREFS
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Cf. A157918, A005843
Sequence in context: A038628 A158638 A016982 this_sequence A100453 A017150 A137880
Adjacent sequences: A157916 A157917 A157918 this_sequence A157920 A157921 A157922
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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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