%I A044812
%S A044812 99,199,299,399,499,599,699,799,899,999,1099,1199,1299,1399,1499,1599,
%T A044812 1699,1799,1899,1999,2099,2199,2299,2399,2499,2599,2699,2799,2899,2999,
%U A044812 3099,3199,3299,3399,3499,3599,3699,3799,3899
%N A044812 Numbers n such that string 9,9 occurs in the base 10 representation of 
               n but not of n+1.
%C A044812 If A=[A158129] 100*n.^2-2*n (n>0, 98, 396, 894,.,. ,.,); Y=[A010692] 
               10 (10, 10, 10,.,); X=[A044812] 100*n-1 (n>0, 99, 199, 299, ,. .,
               ), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 
               99^2-98*10^2=1; 199^2-396*10^2=1; 299^2-894*10^2=1. [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
%H A044812 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               NonRecursions.html">Non Recursions</a>
%F A044812 a(n)=100*n-1 (n>0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%e A044812 For n=1, a(1)=99; n=2, a(2)=199; n=3, a(3)=299 [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Mar 13 2009]
%Y A044812 Cf. A158129, A010692 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%Y A044812 Sequence in context: A043526 A031500 A044431 this_sequence A125820 A008902 
               A008882
%Y A044812 Adjacent sequences: A044809 A044810 A044811 this_sequence A044813 A044814 
               A044815
%K A044812 nonn,base
%O A044812 1,1
%A A044812 Clark Kimberling (ck6(AT)evansville.edu)