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%I #34 Feb 18 2024 08:26:52
%S 11,22,33,44,55,66,77,88,99,100,101,110,111,112,113,114,115,116,117,
%T 118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,
%U 199,200,202,211,212,220,221,222,223,224,225,226,227,228,229,232,233,242
%N Numbers k with at least one duplicate base-10 digit (A107846(k) > 0).
%C Complement of A010784, numbers with distinct base-10 digits, so all numbers greater than 9876543210 (last term of A010784) are terms. a(263)=1001 is the first term not also a term of A044959; a(264)=1002 is the first term not also a term of A084050. The terms of A044959 greater than 9 are a subsequence. The terms of A084050 greater than 90 are a subsequence.
%C A178788(a(n)) = 0; A178787(a(n)) = A178787(a(n)-1); A043537(a(n)) < A109303(a(n)). - _Reinhard Zumkeller_, Jun 30 2010
%C A227362(a(n)) < a(n). - _Reinhard Zumkeller_, Jul 09 2013
%H Reinhard Zumkeller, <a href="/A109303/b109303.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%t Select[Range[300], Max[DigitCount[#]] > 1 &] (* _Harvey P. Dale_, Jan 14 2011 *)
%o (Haskell)
%o a109303 n = a109303_list !! (n-1)
%o a109303_list = filter ((> 0) . a107846) [0..]
%o -- _Reinhard Zumkeller_, Jul 09 2013
%o (Python)
%o def ok(n): s = str(n); return len(set(s)) < len(s)
%o print([k for k in range(243) if ok(k)]) # _Michael S. Branicky_, Nov 22 2021
%Y Cf. A010784 (numbers with distinct digits), A044959 (numbers with no two equally numerous digits), A084050 (numbers with a palindromic permutation of digits), A107846 (number of duplicate digits of n). Also see A062813, which gives the largest number in each base containing all distinct digits.
%K base,easy,nonn
%O 1,1
%A _Rick L. Shepherd_, Jun 24 2005
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