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Search: id:A157659
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| 99, 398, 897, 1596, 2495, 3594, 4893, 6392, 8091, 9990, 12089, 14388, 16887, 19586, 22485, 25584, 28883, 32382, 36081, 39980, 44079, 48378, 52877, 57576, 62475, 67574, 72873, 78372, 84071, 89970, 96069, 102368, 108867, 115566, 122465, 129564
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OFFSET
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1,1
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COMMENT
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If A=[A157659] 100*n.^2-n (99, 398, 897, 1596 ,..,); Y=[A157660] 8000*n-40 (7960, 15960, 23960..,); X=[A157661] 80000*n^2-800*n+1 (79201, 318401, 717601,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 79201^2-99*7960^2=1; 318401^2-398*15960^2=1; 717601^2-897*23960^2=1.
If A=[A157659] 100*n.^2-n (99, 398, 897, ,.,); Y=[A010859] 20 (20, 20, 20,. ,.,); X=[A157955] 200*n-1 (199, 399, 599,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 199^2-99 *20^2=1; 399^2-398*20^2=1; 599^2-897*20^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009]
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LINKS
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Wolfram MathWorld, Pell Equation
Philippe Chevanne, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)=100*n^2-n (n>0)
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EXAMPLE
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For n=1, a(1)=99; n=2, a(2)=398; n=3, a(3)=897
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CROSSREFS
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Cf. A157660, A157661
Cf. A010859, A157955 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009]
Sequence in context: A008882 A156757 A027579 this_sequence A154359 A061366 A135219
Adjacent sequences: A157656 A157657 A157658 this_sequence A157660 A157661 A157662
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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 04 2009
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