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A105279
a(0)=0; a(n) = 10*a(n-1) + 10.
6
0, 10, 110, 1110, 11110, 111110, 1111110, 11111110, 111111110, 1111111110, 11111111110, 111111111110, 1111111111110, 11111111111110, 111111111111110, 1111111111111110, 11111111111111110, 111111111111111110, 1111111111111111110, 11111111111111111110, 111111111111111111110
OFFSET
0,2
COMMENTS
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
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
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
FORMULA
a(n) = (10/9)*(10^n-1), with n>=0.
a(n) = Sum_{k=1..n} 10^k.
Repunits times 10: a(n) = 10 * A002275(n). - Reinhard Zumkeller, Feb 05 2012
From Stefano Spezia, Sep 15 2023: (Start)
O.g.f.: 10*x/((1 - x)*(1 - 10*x)).
E.g.f.: 10*exp(x)*(exp(9*x) - 1)/9. (End)
MATHEMATICA
NestList[10*(# + 1) &, 0, 25] (* Paolo Xausa, Jul 17 2024 *)
PROG
(Magma) [-10/9+(10/9)*10^n: n in [0..20]]; // Vincenzo Librandi, Jul 04 2011
(Haskell)
a105279 n = a105279_list !! n
a105279_list = iterate ((* 10) . (+ 1)) 0
-- Reinhard Zumkeller, Feb 05 2012
CROSSREFS
Row n=10 of A228275.
Partial sums of A178500.
Sequence in context: A288977 A289046 A284021 * A246942 A289371 A289100
KEYWORD
nonn,easy
AUTHOR
Alexandre Wajnberg, Apr 25 2005
STATUS
approved