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Search: id:A158129
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| 98, 396, 894, 1592, 2490, 3588, 4886, 6384, 8082, 9980, 12078, 14376, 16874, 19572, 22470, 25568, 28866, 32364, 36062, 39960, 44058, 48356, 52854, 57552, 62450, 67548, 72846, 78344, 84042, 89940, 96038, 102336, 108834, 115532, 122430, 129528
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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If A=[A158129] 100*n.^2-2*n (n>0, 98, 396, 894,.,. ,.,); Y=[A010692] 10 (10, 10, 10,.,); X=[A044812] 100*n-1 (n>0, 99, 199, 299, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 99^2-98*10^2=1; 199^2-396*10^2=1; 299^2-894*10^2=1. Table beging: Primitive of Pell's equation A X Y Y X A 2 3 2 2 5 6 7 8 3 3 10 11 14 15 4 4 17 18 23 24 5 5 26 27 34 35 6 6 37 38 47 48 7 7 50 51 62 63 8 8 65 66 79 80 9 9 82 83 98 99 10 10 101 102 119 120 11 11 122 123 142 143 12 12 145 146 167 168 13 13 170 171 and so on. (Y=n^2; 4=2*2; 9=3*3)
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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)=98; n=2, a(2)=396; n=3, a(3)=894
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CROSSREFS
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Cf. A010692, A044812
Sequence in context: A038863 A072607 A160828 this_sequence A071319 A088736 A019563
Adjacent sequences: A158126 A158127 A158128 this_sequence A158130 A158131 A158132
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KEYWORD
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nonn,tabl
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009
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