%I A157951
%S A157951 129,257,385,513,641,769,897,1025,1153,1281,1409,1537,1665,1793,1921,
%T A157951 2049,2177,2305,2433,2561,2689,2817,2945,3073,3201,3329,3457,3585,3713,
%U A157951 3841,3969,4097,4225,4353,4481,4609,4737,4865,4993,5121,5249,5377,5505
%N A157951 a(n)=128*n+1 (n>0)
%C A157951 If A=[A031694] 64*n.^2+n (65, 258, 579,.,); Y=[A010855] 16 (16, 16, 16, 
               ,.,); X=[A157951] 128*n+1 (129, 257, 385.,), we have, for all terms, 
               Pell's equation X^2-A*Y^2=1. Example: 129^2-65 *16^2=1; 257^2-258*16^2=1; 
               385^2-579*16^2=1.
%H A157951 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 A157951 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%H A157951 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%F A157951 a(n)=128*n+1 (n>0)
%e A157951 For n=1, a(1)=129; n=2, a(2)=257; n=3, a(3)=385
%Y A157951 Cf. A031694, A010855
%Y A157951 Sequence in context: A060878 A127337 A034072 this_sequence A043383 A036548 
               A046286
%Y A157951 Adjacent sequences: A157948 A157949 A157950 this_sequence A157952 A157953 
               A157954
%K A157951 nonn
%O A157951 1,1
%A A157951 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009