Search: id:A157949
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%I A157949
%S A157949 127,255,383,511,639,767,895,1023,1151,1279,1407,1535,1663,1791,1919,
%T A157949 2047,2175,2303,2431,2559,2687,2815,2943,3071,3199,3327,3455,3583,3711,
%U A157949 3839,3967,4095,4223,4351,4479,4607,4735,4863,4991,5119,5247,5375,5503
%N A157949 a(n)=128*n-1 (n>0)
%C A157949 If A=[A157948] 64*n.^2-n (63, 254, 573,.,); Y=[A010855] 16 (16, 16, 16, 
               ,.,); X=[A157949] 128*n-1 1 (127, 255, 383.,), we have, for all terms, 
               Pell's equation X^2-A*Y^2=1. Example: 127^2-63 *16^2=1; 255^2-254*16^2=1; 
               383^2-573*16^2=1.
%H A157949 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 A157949 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%H A157949 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%F A157949 a(n)=128*n-1 (n>0)
%e A157949 For n=1, a(1)=127; n=2, a(2)=255; n=3, a(3)=383
%Y A157949 Cf. A157948, A010855
%Y A157949 Sequence in context: A142551 A048453 A138127 this_sequence A142165 A031933 
               A080035
%Y A157949 Adjacent sequences: A157946 A157947 A157948 this_sequence A157950 A157951 
               A157952
%K A157949 nonn
%O A157949 1,1
%A A157949 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009

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