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A008591 Multiples of 9: a(n) = 9*n.

%I A008591 #83 Jul 08 2025 12:10:44
%S A008591 0,9,18,27,36,45,54,63,72,81,90,99,108,117,126,135,144,153,162,171,
%T A008591 180,189,198,207,216,225,234,243,252,261,270,279,288,297,306,315,324,
%U A008591 333,342,351,360,369,378,387,396,405,414,423,432,441,450,459,468,477
%N A008591 Multiples of 9: a(n) = 9*n.
%C A008591 An Iraqi tablet dating from the Middle Babylonian period (1400-1100 BC) gives a(1)-a(20), a(30), a(40), and a(50). See CDLI link for images and more information. - _Charles R Greathouse IV_, Jan 21 2017
%C A008591 Apart from 0, numbers whose digital root is 9. - _Halfdan Skjerning_, Mar 15 2018
%C A008591 Also numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 9. - _Stefano Spezia_, Jul 08 2025
%H A008591 Ivan Panchenko, <a href="/A008591/b008591.txt">Table of n, a(n) for n = 0..200</a>
%H A008591 CDLI, <a href="http://cdli.ucla.edu/search/archival_view.php?ObjectID=P254585">MKT 1, 039, HS 0217a</a>
%H A008591 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=321">Encyclopedia of Combinatorial Structures 321</a>
%H A008591 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A008591 Luis Manuel Rivera, <a href="https://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%H A008591 Leo Tavares, <a href="/A008591/a008591.jpg">Illustration: Triangular Frames</a>
%H A008591 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A008591 Complement of A168183; A168182(a(n)) = 0. - _Reinhard Zumkeller_, Nov 30 2009
%F A008591 a(n) = A007953(A002283(n)). - _Reinhard Zumkeller_, Aug 06 2010
%F A008591 From _Vincenzo Librandi_, Dec 24 2010: (Start)
%F A008591 a(n) = 9*n = 2*a(n-1) - a(n-2).
%F A008591 G.f.: 9x/(x-1)^2. (End)
%F A008591 a(n) = A060544(n+1) - A060544(n). - _Leo Tavares_, Jul 17 2022
%F A008591 E.g.f.: 9*x*exp(x). - _Stefano Spezia_, Oct 08 2022
%t A008591 Range[0, 1000, 9] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2011 *)
%o A008591 (PARI) a(n)=9*n \\ _Charles R Greathouse IV_, Jan 30 2012
%o A008591 (Maxima) makelist(9*n,n,0,20); /* _Martin Ettl_, Dec 17 2012 */
%Y A008591 Cf. A008588, A008589, A008590.
%Y A008591 Cf. A168182, A168183.
%Y A008591 Cf. A002283, A007953.
%Y A008591 Cf. A060544.
%K A008591 nonn,easy
%O A008591 0,2
%A A008591 _N. J. A. Sloane_