Search: id:A157955
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%I A157955
%S A157955 199,399,599,799,999,1199,1399,1599,1799,1999,2199,2399,2599,2799,2999,
%T A157955 3199,3399,3599,3799,3999,4199,4399,4599,4799,4999,5199,5399,5599,5799,
%U A157955 5999,6199,6399,6599,6799,6999,7199,7399,7599,7799,7999,8199,8399,8599
%N A157955 a(n)=200*n-1 (n>0)
%C A157955 If A=[A157659] 100*n.^2-n (99, 398, 897, ,.,); Y=[A010859] 20 (20, 20, 
               20,. ,.,); X=[A157955] 200*n-1 (199, 399, 599,. .,), we have, for 
               all terms, Pell's equation X^2-A*Y^2=1. Example: 199^2-99 *20^2=1; 
               399^2-398*20^2=1; 599^2-897*20^2=1.
%H A157955 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 A157955 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A157955 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A157955 a(n)=200*n-1 (n>0)
%e A157955 For n=1, a(1)=199; n=2, a(2)=399; n=3, a(3)=599
%Y A157955 Cf. A157659, A010859
%Y A157955 Sequence in context: A106759 A004926 A004946 this_sequence A033168 A140632 
               A142814
%Y A157955 Adjacent sequences: A157952 A157953 A157954 this_sequence A157956 A157957 
               A157958
%K A157955 nonn
%O A157955 1,1
%A A157955 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009

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