A084050 -id:A084050 - cp's OEIS frontend

A084051 Smallest palindrome corresponding to A084050(n).

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

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

Original entry on oeis.org

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

A276115 Numbers whose digits have a permutation that is a palindrome.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 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, 202, 211, 212, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 232, 233, 242, 244, 252, 255, 262, 266

Offset: 1

Judson Neer, Aug 19 2016

Permutations with leading zeros are not considered as palindromic, thus (for example) 10 is not included in the sequence.

Also numbers in which at most 1 digit occurs an odd number of times and (if there is more than one digit) at least 2 digits are nonzero. - David A. Corneth, Aug 21 2016, corrected by Robert Israel, Aug 31 2016

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A084050 (for a sequence where leading zero numbers are included).

filter:= proc(n) local L,M;
  if n < 10 then return true fi;
  L:= convert(n,base,10);
  M:= [seq(numboccur(j,L),j=0..9)];
  convert(M mod 2, `+`) <= 1 and convert(M[2..-1],`+`)>=2
end proc:
select(filter, [$1..1000]); # Robert Israel, Aug 31 2016

is(n) = {my(v = concat(vecsort(digits(n)), ["a"]), prev=1, odd=0); if(#v>2&&v[#v-2]==0,return(0)); for(i=1,#v-1, if(v[i]!=v[i+1], odd+=(i-prev+1)%2; if(odd==2,return(0)); prev = i + 1)); 1} \\ David A. Corneth, Aug 21 2016

101 inserted by Robert Israel, Aug 31 2016

cp's OEIS Frontend

A084051 Smallest palindrome corresponding to A084050(n).

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

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A276115 Numbers whose digits have a permutation that is a palindrome.

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