Search: id:A010734
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%I A010734
%S A010734 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%T A010734 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%U A010734 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
%N A010734 Constant sequence.
%C A010734 The digital root of 9^n gives the sequence 1,9,9,9,9,... - Cino Hilliard 
               (hillcino368(AT)gmail.com), Dec 31 2004
%C A010734 If A=[A031433] 81*n.^2+2*n (n>0, 83, 328, 735,.,. ,.,); Y=[A010734] 9 
               (9,9,9,.,..,); X=[A158123] 81*n+1 (n>0, 82, 163, 244, ,. .,), we 
               have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 82^2-83*9^2=1; 
               163^2-328*9^2=1; 244^2-735*9^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%C A010734 If A=[A157507] 81*n.^2-2*n (n>0, 79, 320, 723,.,. ,.,); Y=[A010734] 9 
               (9,9,9,.,..,); X=[A044712] 81*n-1 (n>0, 80, 161, 242, ,. .,), we 
               have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 80^2-79*9^2=1; 
               161^2-320*9^2=1; 242^2-723*9^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%H A010734 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A010734 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A010734 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=1017">
               Encyclopedia of Combinatorial Structures 1017</a>
%Y A010734 Cf. A031433, A158123 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%Y A010734 Cf. A157507, A044712 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%Y A010734 Sequence in context: A116667 A137577 A099646 this_sequence A066568 A106326 
               A088471
%Y A010734 Adjacent sequences: A010731 A010732 A010733 this_sequence A010735 A010736 
               A010737
%K A010734 nonn
%O A010734 0,1
%A A010734 N. J. A. Sloane (njas(AT)research.att.com).

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