Search: id:A158129
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%I A158129
%S A158129 98,396,894,1592,2490,3588,4886,6384,8082,9980,12078,14376,16874,19572,
%T A158129 22470,25568,28866,32364,36062,39960,44058,48356,52854,57552,62450,
%U A158129 67548,72846,78344,84042,89940,96038,102336,108834,115532,122430,129528
%N A158129 a(n)=100*n^2-2*n (n>0)
%C A158129 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)
%H A158129 Edward Everett Withford, <a href="http://quod.lib.umich.edu/cgi/t/text/
               text-idx?c=umhistmath;cc=umhistmath;idno=abv2773.0001.001;view=toc">
               Pell Equation</a>
%H A158129 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A158129 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A158129 a(n)=100*n^2-2*n (n>0)
%e A158129 For n=1, a(1)=98; n=2, a(2)=396; n=3, a(3)=894
%Y A158129 Cf. A010692, A044812
%Y A158129 Sequence in context: A038863 A072607 A160828 this_sequence A071319 A088736 
               A019563
%Y A158129 Adjacent sequences: A158126 A158127 A158128 this_sequence A158130 A158131 
               A158132
%K A158129 nonn,tabl
%O A158129 1,1
%A A158129 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009

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