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 A010785 Repdigit numbers, or numbers with repeated digits. 60

%I

%S 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,222,333,444,555,

%T 666,777,888,999,1111,2222,3333,4444,5555,6666,7777,8888,9999,11111,

%U 22222,33333,44444,55555,66666,77777,88888,99999,111111,222222

%N Repdigit numbers, or numbers with repeated digits.

%C A037904(a(n)) = 0. - _Reinhard Zumkeller_, Dec 14 2007

%C Complement of A139819. - David Wasserman, May 21 2008

%C Subsequence of A134336 and of A178403; A178401(a(n))>0. [From _Reinhard Zumkeller_, May 27 2010]

%C For n > 0: A193459(a(n)) = A000005(a(n)), subsequence of A193460;

%C for n > 10: a(n) mod 10 = floor(a(n)/10) mod 10, A010879(n)=A010879(A059995(n)). [_Reinhard Zumkeller_, Jul 26 2011]

%C A202022(a(n)) = 1. [_Reinhard Zumkeller_, Dec 09 2011]

%H _Reinhard Zumkeller_, <a href="/A010785/b010785.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repdigit.html">Repdigit</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Repdigit">Repdigit</a>

%F a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=6, a(7)=7, a(8)=8, a(9)=9, a(10)=11, a(11)=22, a(12)=33, a(13)=44, a(14)=55, a(15)=66, a(16)=77, a(17)=88, a(n)=11*a(n-9)-10*a(n-18) [From Harvey P. Dale, Dec 28 2011]

%t fQ[n_]:=Module[{id=IntegerDigits[n]}, Length[Union[id]]==1]; Select[Range[0,10000], fQ] (* Vladimir Joseph Stephan Orlovsky, 29 Dec 2010 *)

%t Union[FromDigits/@Flatten[Table[PadRight[{},i,n],{n,0,9},{i,6}],1]] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,-10},{0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88},40] (* From Harvey P. Dale, Dec 28 2011 *)

%o (PARI) a(n)=10^((n+8)\9)\9*((n-1)%9+1) \\ _Charles R Greathouse IV_, Jun 15 2011

%o a010785 n = a010785_list !! n

%o a010785_list = 0 : r [1..9] where

%o r (x:xs) = x : r (xs ++ [10*x + x `mod` 10])

%o -- _Reinhard Zumkeller_, Jul 26 2011

%K nonn,base,easy,nice,changed

%O 0,3

%A _N. J. A. Sloane_.

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