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Search: id:A157664
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| A157664 |
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a(n)=80000*n^2+800*n+1 (n>0) |
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+0
3
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| 80801, 321601, 722401, 1283201, 2004001, 2884801, 3925601, 5126401, 6487201, 8008001, 9688801, 11529601, 13530401, 15691201, 18012001, 20492801, 23133601, 25934401, 28895201, 32016001, 35296801, 38737601, 42338401, 46099201
(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=[A055438] 100*n.^2+n (101, 402, 903, ,..,); Y=[A157663] 8000*n+40 (8040, 16040, 24040,..,); X=[A157664] 80000*n^2+800*n+1 (80801, 321601, 722401,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 80801^2-101*8040^2=1; 321601^2-402*16040^2=1; 722401^2-903*24040^2=1.
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LINKS
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Philippe Chevanne, Pell Equation
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FORMULA
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a(n)=80000*n^2+800*n+1 (n>0)
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EXAMPLE
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Fr n=1, a(1)=80801; n=2, a(2)=321601; n=3, a(3)=722401
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CROSSREFS
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Cf. A055438, A157663
Sequence in context: A095946 A050517 A069304 this_sequence A064001 A029752 A043608
Adjacent sequences: A157661 A157662 A157663 this_sequence A157665 A157666 A157667
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vinceno.librandi(AT)tin.it), Mar 04 2009
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