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A158421 a(n) = 1024*n - 1.

%I A158421 #18 Sep 08 2022 08:45:43
%S A158421 1023,2047,3071,4095,5119,6143,7167,8191,9215,10239,11263,12287,13311,
%T A158421 14335,15359,16383,17407,18431,19455,20479,21503,22527,23551,24575,
%U A158421 25599,26623,27647,28671,29695,30719,31743,32767,33791,34815,35839
%N A158421 a(n) = 1024*n - 1.
%C A158421 The identity (1024*n-1)^2-(1024*n^2-2*n)*(32)^2=1 can be written as a(n)^2-A158420(n)*(32)^2=1.
%H A158421 Vincenzo Librandi, <a href="/A158421/b158421.txt">Table of n, a(n) for n = 1..10000</a>
%H A158421 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a>
%H A158421 E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(32^2*t-2)).
%H A158421 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A158421 a(n) = 2*a(n-1)-a(n-2).
%F A158421 G.f.: x*(1023+x)/(1-x)^2.
%t A158421 LinearRecurrence[{2,-1},{1023,2047},50]
%o A158421 (Magma) I:=[1023, 2047]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o A158421 (PARI) a(n) = 1024*n - 1.
%Y A158421 Cf. A158420.
%K A158421 nonn,easy
%O A158421 1,1
%A A158421 _Vincenzo Librandi_, Mar 18 2009