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Search: id:A157507
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| 79, 320, 723, 1288, 2015, 2904, 3955, 5168, 6543, 8080, 9779, 11640, 13663, 15848, 18195, 20704, 23375, 26208, 29203, 32360, 35679, 39160, 42803, 46608, 50575, 54704, 58995, 63448, 68063, 72840, 77779, 82880, 88143, 93568, 99155, 104904
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OFFSET
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1,1
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COMMENT
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If A=[A157507] 81*n.^2-2*n (79,320,723,1288,.,); Y=[A157508] 1458*n-18 (1440,2898,4356..,); X=[A157509] 13122*n^2-324*n+1 (12799,51841,117127,.,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 12799^2-79*1440^2=1; 51841^2-320*2898^2=1; 117127^2-723*4356^2=1.
If A=[A157507] 81*n.^2-2*n (n>0, 79, 320, 723,.,. ,.,); Y=[A010734] 9 (9,9,9,.,..,); X=[A044712] 81*n-1 (n>0, 80, 161, 242, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 80^2-79*9^2=1; 161^2-320*9^2=1; 242^2-723*9^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
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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)=81*n^2-2*n (n>0)
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EXAMPLE
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For n=1, a(1)=79; n=2, a(2)=320; n=3, a(3)=723
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CROSSREFS
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Cf. A157508, A157509
Cf. A010734, A044712 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
Sequence in context: A082077 A158769 A158774 this_sequence A142897 A142330 A007254
Adjacent sequences: A157504 A157505 A157506 this_sequence A157508 A157509 A157510
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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 02 2009
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