A044959 -id:A044959 - cp's OEIS frontend

A109303 Numbers k with at least one duplicate base-10 digit (A107846(k) > 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

Rick L. Shepherd, Jun 24 2005

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

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.

a109303 n = a109303_list !! (n-1)
a109303_list = filter ((> 0) . a107846) [0..]
-- Reinhard Zumkeller, Jul 09 2013

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

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

A084050 Numbers n such that at least one permutation of the digits of n yields a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 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

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 26 2003

Union of A037124 and numbers with at most one decimal digit occurring an odd number of times. a(281)=1001 is the first term greater than 90 not also a term of A044959. The terms greater than 90 are a subsequence of A109303. - Rick L. Shepherd, Jun 24 2005

Cf. A044959, A084051.

Cf. A037124 (numbers with only one nonzero digit), A109303 (numbers with at least one duplicate digit).

Corrected by Rick L. Shepherd, Jun 24 2005

A353181 Numbers in which more than half of the digits are the same.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 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

Offset: 1

Zhining Yang, Apr 29 2022

Same as A044959 for terms <= 1000, and then differing at A044959(272) = 1001 which is not a term here (the next instead a(272) = 1011).

			1211 is a term: it has 4 digits, 3 of which are 1's, and 3/4 > 1/2.
1212 is not a term: it has 4 digits, no one of which appears more than twice.

Zhining Yang, Table of n, a(n) for n = 1..30000

Cf. A109303, A044959.

Select[Range[300], Max[DigitCount[#]] > IntegerLength[#]/2 &]

def ok(k):
    t=str(k)
    return(max(t.count(str(i)) for i in range(10))>(len(t)//2))
print([n for n in range(1, 201) if ok(n)])

A048321 Reading a(n) expansion from left to right, run lengths strictly decrease.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 440, 441, 442, 443, 444, 445, 446, 447, 448

Offset: 1

Patrick De Geest, Feb 15 1999

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

Cf. A037013, A043636, A043713, A044821, A044959.

import Data.List (group)
a048321 n = a048321_list !! (n-1)
a048321_list = filter f [0..] where
   f x = all (< 0) $ zipWith (-) (tail zs) zs
         where zs =  map length $ group $ show x
-- Reinhard Zumkeller, May 01 2015

A084051 Smallest palindrome corresponding to A084050(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 2, 22, 3, 33, 4, 44, 5, 55, 6, 66, 7, 77, 8, 88, 9, 99, 1, 101, 11, 111, 121, 131, 141, 151, 161, 171, 181, 191, 121, 212, 131, 313, 141, 414, 151, 515, 161, 616, 171, 717, 181, 818, 191, 919, 2, 202, 121, 212, 22, 212, 222, 232, 242, 252

Offset: 0

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 26 2003

Cf. A044959, A084050.

Corrected by Rick L. Shepherd, Jun 24 2005

A121977 Numbers with a distinct frequency for each decimal digit.

Original entry on oeis.org

100000000011111112222222333333444445555666778, 100000000011111112222222333333444445555666779, 100000000011111112222222333333444445555666787, 100000000011111112222222333333444445555666788, 100000000011111112222222333333444445555666797, 100000000011111112222222333333444445555666799, 100000000011111112222222333333444445555666877, 100000000011111112222222333333444445555666878

Offset: 1

Franklin T. Adams-Watters, Sep 05 2006

			100000000011111112222222333333444445555666778 has 9 0's, 8 1's, 7 2's, 6 3's, 5 4's, 4 5's, 3 6's, 2 7's, 1 8 and 0 9's. 121 is not in the sequence because there are eight digits it has zero of.

Cf. A044959, A044951.

Subsequence of A179239.

A048307 Numbers whose decimal expansions, read from left to right, have run lengths that strictly increase.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 300, 311, 322, 333, 344, 355, 366, 377, 388, 399, 400, 411, 422, 433, 444, 455, 466, 477, 488

Offset: 0

Patrick De Geest, Feb 15 1999

Cf. A037015, A043636, A043713, A044821, A044959.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Mathematica

Python

A084050 Numbers n such that at least one permutation of the digits of n yields a palindrome.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A353181 Numbers in which more than half of the digits are the same.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

A048321 Reading a(n) expansion from left to right, run lengths strictly decrease.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

A084051 Smallest palindrome corresponding to A084050(n).

Views

Author

Keywords

Crossrefs

Extensions

A121977 Numbers with a distinct frequency for each decimal digit.

Views

Author

Keywords

Examples

Crossrefs

A048307 Numbers whose decimal expansions, read from left to right, have run lengths that strictly increase.

Views

Author

Keywords

Crossrefs