%I A156842
%S A156842 263,46,887,2786,5743,9758,14831,20962,28151,36398,45703,56066,67487,
%T A156842 79966,93503,108098,123751,140462,158231,177058,196943,217886,239887,
%U A156842 262946,287063,312238,338471,365762,394111,423518,453983,485506,518087
%N A156842 a(n)=529*n^2-746*n+263
%C A156842 Arises in solving Pell equations of the form X^2 - A*Y^2 = 1.
%C A156842 Let n=[A156849] (156,373,685,902,...,) =n^2-2=0 mod (23^2). If A=[A156841] 
               (46,263,1538,3871,.,) = 529*n^2-312*n+46 or A=[156842] (263,46,887,
               2787) =(529*n^2-746*n+263 , Y=23*n, or [A156845] (3588,15755,27922,
               ...,) = 12167*n-8579, or Y=[A156846] (8579,20746,32913,...,) =12167*n-3588, 
               and X=279841*n^2-165048*n+24335 [A156843] (24335,139128,813603,...,
               ) or X=[A156844] =279841*n^2-394634*n+139128 (139128,24335,469224,
               1473795,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. 
               Example: For n=156, A=46, Y=3588, X=24335, 24335^2-46*3588^2=1 ; 
               n=373, A=263, Y=8579, X=139128; 139128^2-263*8579^2=1; n=685, A=887, 
               Y=15755, X=469224; 469224^2-887*15755^2=1; n=902, A=1538, Y=20746, 
               X=813603; 813603^2-1538*20746^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 20 2009]
%H A156842 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&tstart=0">
               X^2-AY^2=1</a> [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 20 2009]
%e A156842 For n=0, a(0)=263; n=1, a(1)=46; n=2, a(2)=887; n=3, a(3)=2786
%Y A156842 Cf. A156841
%Y A156842 Cf. A156843, A156844, A156845, A156846, A156849 [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Feb 20 2009]
%Y A156842 Sequence in context: A063364 A028536 A045179 this_sequence A052033 A105008 
               A142754
%Y A156842 Adjacent sequences: A156839 A156840 A156841 this_sequence A156843 A156844 
               A156845
%K A156842 nonn
%O A156842 1,1
%A A156842 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 17 2009