%I #14 Feb 19 2023 09:18:00
%S 1,101,1001,10001,100001,112233,10000001,100122,10000111,1111112222,
%T 100000000001,1000122,10000000000001,1000011111,10011122,1000000111,
%U 100000000000000001,10000122,10000000000000000001,1111112233,11111111112222,10000000000000000000001,100000000000000000000001,11223344
%N Smallest number whose digits can be permuted to get exactly n distinct palindromes.
%C a(n) <= 10^n + 1.
%C Any number C(i+j,j) is the number of palindromes from 2i 1's and 2j 2's, so in particular a(10) <= 1111112222 and a(15) <= 111111112222. If a number in this sequence has an odd number of digits, the odd digit must be 0 or 1, with all other digits in pairs; if the number of digits is even, all must be in pairs. The counts of the nonzero digits must be monotonically decreasing (i.e., at least as many 1's as 2's, etc.) - _Franklin T. Adams-Watters_, Oct 26 2006
%H Max Alekseyev, <a href="/A082276/b082276.txt">Table of n, a(n) for n = 1..130</a>
%e 101 gives two palindromes: 101 and 011 = 11 hence a(2) = 101.
%e a(6) = 112233, the digit permutation gives six palindromes: 123321, 132231, 213312, 231132, 312213, 321123.
%Y Cf. A082274, A082275.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Apr 13 2003
%E Terms to a(9), and a(12), a(18), a(24), a(30) from _Franklin T. Adams-Watters_, Oct 26 2006
%E Terms from a(10) onward from _Max Alekseyev_, Feb 17 2023