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Search: id:A157620
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| A157620 |
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a(n)=781250*n^2-1107500*n+392499 (n>0) |
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+0
3
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| 66249, 1302499, 4101249, 8462499, 14386249, 21872499, 30921249, 41532499, 53706249, 67442499, 82741249, 99602499, 118026249, 138012499, 159561249, 182672499, 207346249, 233582499, 261381249, 290742499, 321666249, 354152499
(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=[A157618] 625*n.^2-886*n +314 (53, 1042, 3281, 6770,..,); Y=[A157619] 31250*n-22150 (9100, 40350, 71600..,); X=[A157620] 781250*n^2-1107500*n+392499 (66249, 1302499, 4101249,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 66249^2-53*9100^2=1; 1302499^2-1042*40350^2=1; 4101249^2-3281*71600^2=1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=781250*n^2-1107500*n+392499 (n>0)
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EXAMPLE
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For n=1, a(1)=66249; n=2, a(2)=1302499; n=3, a(3)=4101249
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CROSSREFS
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Cf. A157618, A157619
Sequence in context: A032781 A156424 A092376 this_sequence A164129 A043591 A022256
Adjacent sequences: A157617 A157618 A157619 this_sequence A157621 A157622 A157623
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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 03 2009
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