A109303 Numbers n with at least one duplicate base-10 digit (A107846(n) > 0).

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 133, 141, 144, 151, 155, 161, 166, 171, 177, 181, 188, 191, 199, 200, 202, 211, 212, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 232, 233, 242

Offset

1,1

Comments

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.

A178788(a(n))=0; A178787(a(n))=A178787(a(n)-1); A043537(a(n))<A109303(a(n)). - Reinhard Zumkeller, Jun 30 2010

A227362(a(n)) < a(n). - Reinhard Zumkeller, Jul 09 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Maple

A109303:=proc(q) local a, b, c, n;
for n from 0 to q do a:=n; b:=[];
  while a>0 do c:=a mod 10; b:=[op(b), c]; a:=trunc(a/10); od;
  a:=nops(b); b:=nops({op(b)}); if a-b>0 then print(n); fi;
od; end: A109303(10^4); # Paolo P. Lava, Apr 18 2013

Mathematica

Select[Range[300], Max[DigitCount[#]] > 1 &] (* Harvey P. Dale, Jan 14 2011 *)

Prog

(Haskell)
a109303 n = a109303_list !! (n-1)
a109303_list = filter ((> 0) . a107846) [0..]
-- Reinhard Zumkeller, Jul 09 2013
(Python)
def ok(n): s = str(n); return len(set(s)) < len(s)
print([k for k in range(243) if ok(k)]) # Michael S. Branicky, Nov 22 2021

Crossrefs

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.

Sequence in context: A087346 A060314 A337240 * A338214 A068520 A171901

Adjacent sequences: A109300 A109301 A109302 * A109304 A109305 A109306

Keyword

base,easy,nonn

Author

Rick L. Shepherd, Jun 24 2005

Status

approved