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Search: id:A158127
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| 102, 404, 906, 1608, 2510, 3612, 4914, 6416, 8118, 10020, 12122, 14424, 16926, 19628, 22530, 25632, 28934, 32436, 36138, 40040, 44142, 48444, 52946, 57648, 62550, 67652, 72954, 78456, 84158, 90060, 96162, 102464, 108966, 115668, 122570
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OFFSET
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1,1
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COMMENT
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If A=[A158127] 100*n.^2+2*n (n>0, 102, 404, 906,.,. ,.,); Y=[A010692] 10 (10, 10, 10,.,); X=[A158128] 100*n+1 (n>0, 101, 201, 301, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 101^2-102*10^2=1; 201^2-404*10^2=1; 301^2-906*10^2=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)=100*n^2+2*n (n>0)
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EXAMPLE
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For n=1, a(1)=102; n=2, a(2)=404; n=3, a(3)=906
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CROSSREFS
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Cf, A010692, A158128
Sequence in context: A160850 A140062 A127655 this_sequence A151964 A088805 A163435
Adjacent sequences: A158124 A158125 A158126 this_sequence A158128 A158129 A158130
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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 13 2009
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