A082810 Palindromes in which every digit occurs with equal frequency.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003, 3113, 3223, 3333, 3443

Offset: 1

Author

Amarnath Murthy, Apr 21 2003

Keywords

• base
• easy
• nonn

Comments

A superset of A010785. Can someone calculate the index of a term k having d digits? There are terms like 1, 2, 3, 4, 5, 6, 7, 8, 9, 1331, 2442, 3553, ... which have the property that a(31) = 1331, a(42) = 2442, a(53) = 3553 etc. Are there infinitely many such terms?

The additional terms with that property, up to a(100000), are: a(64) = 4664, a(75) = 5775, a(86) = 6886, a(97) = 7997, a(749) = 947749, a(4978) = 87944978, a(46581) = 185640046581. - Georg Fischer, Jan 12 2022

Examples

			132231 is a term.
		

Links

• Georg Fischer, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113, A010785, A266279.