0,1

The digital root of 9^n gives the sequence 1,9,9,9,9,... - Cino Hilliard (hillcino368(AT)gmail.com), Dec 31 2004

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]

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]

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1017

Cf. A031433, A158123 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]

Cf. A157507, A044712 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]

Sequence in context: A116667 A137577 A099646 this_sequence A066568 A106326 A088471

Adjacent sequences: A010731 A010732 A010733 this_sequence A010735 A010736 A010737

nonn

N. J. A. Sloane (njas(AT)research.att.com).