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

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Apart from 0, numbers whose digital root is 9. - Halfdan Skjerning, Mar 15 2018

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

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..200
• CDLI, MKT 1, 039, HS 0217a
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 321
• Tanya Khovanova, Recursive Sequences
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• Leo Tavares, Illustration: Triangular Frames
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008588, A008589, A008590.

Cf. A168182, A168183.

Cf. A002283, A007953.

Cf. A060544.

Programs

Mathematica

Range[0, 1000, 9] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)

Maxima

makelist(9*n,n,0,20); /* Martin Ettl, Dec 17 2012 */

PARI

a(n)=9*n \\ Charles R Greathouse IV, Jan 30 2012

Formula

Complement of A168183; A168182(a(n)) = 0. - Reinhard Zumkeller, Nov 30 2009

a(n) = A007953(A002283(n)). - Reinhard Zumkeller, Aug 06 2010

From Vincenzo Librandi, Dec 24 2010: (Start)

a(n) = 9*n = 2*a(n-1) - a(n-2).

G.f.: 9x/(x-1)^2. (End)

a(n) = A060544(n+1) - A060544(n). - Leo Tavares, Jul 17 2022

E.g.f.: 9*x*exp(x). - Stefano Spezia, Oct 08 2022