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A067251 Numbers with no trailing zeros in decimal representation. 21

%I

%S 1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,

%T 29,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,51,52,53,54,

%U 55,56,57,58,59,61,62,63,64,65,66,67,68,69,71,72,73,74,75,76,77,78,79,81,82,83,84,85,86,87,88,89,91,92,93,94,95,96,97,98,99,101,102,103,104

%N Numbers with no trailing zeros in decimal representation.

%C Or, decimated numbers: every 10th number has been omitted from the natural numbers. - _Cino Hilliard_, Feb 21 2005. For example, The 10th number starting with 1 is 10 and is missing from the table because it was decimated.

%C The word "decimated" can be interpreted in several ways and should be used with caution. - _N. J. A. Sloane_, Feb 21 2005

%C a(n) mod 10 > 0 for all n.

%C Not the same as A052382, as 101 is included.

%C A004086(A004086(a(n)) = a(n).

%C Numbers in here but not in A043095 are 81, 91, 92, 93, 94,... for example. - _R. J. Mathar_, Sep 30 2008

%C Complement of A008592; A168184(a(n)) = 1. - _Reinhard Zumkeller_, Nov 30 2009

%H Reinhard Zumkeller, <a href="/A067251/b067251.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1).

%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.

%F a(n) = n + floor((n-1)/9).

%F From _Colin Barker_, Sep 28 2015: (Start)

%F a(n) = a(n-1) + a(n-9) - a(n-10) for n>10.

%F G.f.: x*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)).

%F (End)

%t DeleteCases[Range[110],_?(Divisible[#,10]&)] (* _Harvey P. Dale_, May 16 2016 *)

%o (PARI) f(n) = for(x=1,n,if(x%10,print1(x","))) - _Cino Hilliard_, Feb 21 2005

%o (PARI) Vec(x*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)/((x-1)^2*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ _Colin Barker_, Sep 28 2015

%o (Haskell)

%o a067251 n = a067251_list !! (n-1)

%o a067251_list = filter ((> 0) . flip mod 10) [0..]

%o -- _Reinhard Zumkeller_, Jul 11 2015, Dec 29 2011

%Y Cf. A076641 (reversed).

%Y Cf. A004086, A008592, A043095, A052382, A168184.

%K nonn,base,easy

%O 1,2

%A _Reinhard Zumkeller_, Mar 10 2002

%E Edited by _N. J. A. Sloane_, Sep 06 2008 at the suggestion of _R. J. Mathar_

%E Typos corrected in a comment line by _Reinhard Zumkeller_, Apr 04 2010

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)