

A067251


Numbers with no trailing zeros in decimal representation.


34



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

1,2


COMMENTS

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.
The word "decimated" can be interpreted in several ways and should be used with caution.  N. J. A. Sloane, Feb 21 2005
a(n) mod 10 > 0 for all n.
Not the same as A052382, as 101 is included.
Numbers in here but not in A043095 are 81, 91, 92, 93, 94,... for example.  R. J. Mathar, Sep 30 2008
The integers 100*a(n) are precisely the numbers whose square ends with exactly 4 identical digits while the integers 10*a(n) form just a subsequence of the numbers whose square ends with exactly 2 identical digits (A346678).  Bernard Schott, Oct 04 2021


LINKS

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,1).


FORMULA

a(n) = n + floor((n1)/9).
a(n) = a(n1) + a(n9)  a(n10) for n>10.
G.f.: x*(x+1)*(x^4x^3+x^2x+1)*(x^4+x^3+x^2+x+1) / ((x1)^2*(x^2+x+1)*(x^6+x^3+1)).
(End)


MAPLE



MATHEMATICA

DeleteCases[Range[110], _?(Divisible[#, 10]&)] (* Harvey P. Dale, May 16 2016 *)


PROG

(PARI) f(n) = for(x=1, n, if(x%10, print1(x", "))) \\ Cino Hilliard, Feb 21 2005
(PARI) Vec(x*(x+1)*(x^4x^3+x^2x+1)*(x^4+x^3+x^2+x+1)/((x1)^2*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ Colin Barker, Sep 28 2015
(Haskell)
a067251 n = a067251_list !! (n1)
a067251_list = filter ((> 0) . flip mod 10) [0..]
(Python)
def a(n): return n + (n1)//9


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



EXTENSIONS



STATUS

approved



