A082276 Smallest number whose digits can be permuted to get exactly n distinct palindromes.

1, 101, 1001, 10001, 100001, 112233, 10000001, 100122, 10000111, 1111112222, 100000000001, 1000122, 10000000000001, 1000011111, 10011122, 1000000111, 100000000000000001, 10000122, 10000000000000000001, 1111112233, 11111111112222, 10000000000000000000001, 100000000000000000000001, 11223344

Offset

1,2

Comments

a(n) <= 10^n + 1.

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

Links

Max Alekseyev, Table of n, a(n) for n = 1..130

Example

101 gives two palindromes: 101 and 011 = 11 hence a(2) = 101.
a(6) = 112233, the digit permutation gives six palindromes: 123321, 132231, 213312, 231132, 312213, 321123.

Crossrefs

Cf. A082274, A082275.

Sequence in context: A242138 A171764 A164842 * A069597 A139535 A139536

Adjacent sequences: A082273 A082274 A082275 * A082277 A082278 A082279

Keyword

base,nonn

Author

Amarnath Murthy, Apr 13 2003

Extensions

Terms to a(9), and a(12), a(18), a(24), a(30) from Franklin T. Adams-Watters, Oct 26 2006

Terms from a(10) onward from Max Alekseyev, Feb 17 2023

Status

approved