|
%I #20 Sep 08 2022 08:45:43
%S 530,1059,1588,2117,2646,3175,3704,4233,4762,5291,5820,6349,6878,7407,
%T 7936,8465,8994,9523,10052,10581,11110,11639,12168,12697,13226,13755,
%U 14284,14813,15342,15871,16400,16929,17458,17987,18516,19045,19574
%N 529n + 1.
%C The identity (529*n+1)^2-(529*n^2+2*n)*(23)^2=1 can be written as a(n)^2-A158367(n)*(23)^2=1.
%H Vincenzo Librandi, <a href="/A158368/b158368.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">X^2-AY^2=1</a>
%H 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*(23^2*t+2)).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: x*(530-x)/(1-x)^2.
%F a(n) = 2*a(n-1)-a(n-2).
%t LinearRecurrence[{2,-1},{530,1059},50]
%t 529*Range[40]+1 (* _Harvey P. Dale_, Nov 02 2017 *)
%o (Magma) I:=[530, 1059]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n) = 529*n + 1.
%Y Cf. A158367.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 17 2009
|
