%N Smallest number whose digits can be permuted to get exactly n distinct palindromes.
%C Note that 10^n + 1 is always an upper bound.
%C a(12) = 1000122, a(18) = 10000122, a(30) = 10012233; probably a(24) = 11223344. 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
%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.
%A _Amarnath Murthy_, Apr 13 2003
%E More terms from _Franklin T. Adams-Watters_, Oct 26 2006