This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105279 #52 Jun 19 2025 00:26:31
%S A105279 0,10,110,1110,11110,111110,1111110,11111110,111111110,1111111110,
%T A105279 11111111110,111111111110,1111111111110,11111111111110,
%U A105279 111111111111110,1111111111111110,11111111111111110,111111111111111110,1111111111111111110,11111111111111111110,111111111111111111110
%N A105279 a(0)=0; a(n) = 10*a(n-1) + 10.
%C A105279 a(n) is the smallest even number with digits in {0,1} having digit sum n; in other words, the base 10 reading of the binary string of A000918(n). Cf. A069532. - _Jason Kimberley_, Nov 02 2011
%C A105279 Also, except for a(0), the binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 645", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - _Robert Price_, Jul 19 2017
%D A105279 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A105279 Vincenzo Librandi, <a href="/A105279/b105279.txt">Table of n, a(n) for n = 0..100</a>
%H A105279 Robert Price, <a href="/A105279/a105279.tmp.txt">Diagrams of first 20 stages of the Cellular Automata</a>.
%H A105279 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.
%H A105279 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>.
%H A105279 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>.
%H A105279 Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</a>.
%H A105279 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>.
%H A105279 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>.
%H A105279 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>.
%H A105279 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A105279 a(n) = (10/9)*(10^n - 1), with n>=0.
%F A105279 a(n) = Sum_{k=1..n} 10^k.
%F A105279 Repunits times 10: a(n) = 10 * A002275(n). - _Reinhard Zumkeller_, Feb 05 2012
%F A105279 From _Stefano Spezia_, Sep 15 2023: (Start)
%F A105279 O.g.f.: 10*x/((1 - x)*(1 - 10*x)).
%F A105279 E.g.f.: 10*exp(x)*(exp(9*x) - 1)/9. (End)
%F A105279 From _Elmo R. Oliveira_, Jun 18 2025: (Start)
%F A105279 a(n) = 11*a(n-1) - 10*a(n-2).
%F A105279 a(n) = A124166(n)/10.
%F A105279 a(n) = A161770(n)/100 for n >= 1. (End)
%t A105279 NestList[10*(# + 1) &, 0, 25] (* _Paolo Xausa_, Jul 17 2024 *)
%o A105279 (Magma) [-10/9+(10/9)*10^n: n in [0..20]]; // _Vincenzo Librandi_, Jul 04 2011
%o A105279 (Haskell)
%o A105279 a105279 n = a105279_list !! n
%o A105279 a105279_list = iterate ((* 10) . (+ 1)) 0
%o A105279 -- _Reinhard Zumkeller_, Feb 05 2012
%Y A105279 Cf. A000918, A002275, A029858, A052379, A052386, A069532, A080674, A124166, A161770.
%Y A105279 Row n=10 of A228275.
%Y A105279 Partial sums of A178500.
%K A105279 nonn,easy
%O A105279 0,2
%A A105279 _Alexandre Wajnberg_, Apr 25 2005