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
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
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).
FORMULA
a(n) = n + floor((n-1)/9).
a(n) mod 10 > 0 for all n.
A168184(a(n)) = 1. - Reinhard Zumkeller, Nov 30 2009
From Colin Barker, Sep 28 2015: (Start)
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)
Sum_{n>=1} (-1)^(n+1)/a(n) = (1/20 + 1/sqrt(5) - sqrt(1+2/sqrt(5))/5) * Pi. - Amiram Eldar, May 11 2025
MAPLE
S := seq(n + floor((n-1)/9), n=1..100); # Bernard Schott, Oct 04 2021
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^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
(PARI) a(n)= n+(n-1)\9 \\ Ruud H.G. van Tol, Jan 23 2026
(Haskell)
a067251 n = a067251_list !! (n-1)
a067251_list = filter ((> 0) . flip mod 10) [0..]
-- Reinhard Zumkeller, Jul 11 2015, Dec 29 2011
(Python)
def a(n): return n + (n-1)//9
print([a(n) for n in range(1, 95)]) # Michael S. Branicky, Oct 04 2021
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Zumkeller, Mar 10 2002
EXTENSIONS
Edited by N. J. A. Sloane, Sep 06 2008 at the suggestion of R. J. Mathar
Typos corrected in a comment line by Reinhard Zumkeller, Apr 04 2010
STATUS
approved