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A067251
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Numbers with no trailing zeros in decimal representation.
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34
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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
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1,2
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COMMENTS
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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
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).
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FORMULA
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a(n) = n + floor((n-1)/9).
a(n) = a(n-1) + a(n-9) - a(n-10) for n>10.
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)).
(End)
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MAPLE
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MATHEMATICA
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DeleteCases[Range[110], _?(Divisible[#, 10]&)] (* Harvey P. Dale, May 16 2016 *)
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PROG
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(PARI) f(n) = for(x=1, n, if(x%10, print1(x", "))) \\ Cino Hilliard, Feb 21 2005
(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
(Haskell)
a067251 n = a067251_list !! (n-1)
a067251_list = filter ((> 0) . flip mod 10) [0..]
(Python)
def a(n): return n + (n-1)//9
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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