A056524 Palindromes with even number of digits.

11, 22, 33, 44, 55, 66, 77, 88, 99, 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, 3553, 3663, 3773, 3883, 3993, 4004, 4114, 4224, 4334, 4444, 4554

Offset: 1

Author

Henry Bottomley, Jun 16 2000

Keywords

• base
• easy
• nonn

Comments

Concatenation of n with reverse of n (keeping leading zeros in the reverse).

A178788(a(n)) = 0 for n > 1. - Reinhard Zumkeller, Jun 30 2010

All of the terms are divisible by eleven. - James Burling, Aug 08 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A002113, A004086, A056525, A066492.

Cf. A020338, A055642, A178788.

Cf. A110745 (permutation).

Programs

Haskell

a056524 n = a056524_list !! (n-1)
a056524_list = [read (ns ++ reverse ns) :: Integer |
                n <- [0..], let ns = show n]
-- Reinhard Zumkeller, Dec 28 2011

Mathematica

d[n_]:=IntegerDigits[n]; Table[FromDigits[Join[x=d[n],Reverse[x]]],{n,45}] (* Jayanta Basu, May 29 2013 *)
Select[Flatten[Table[Range[10^n,10^(n+1)-1],{n,1,3,2}]],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 22 2018 *)

Python

def a(n): s = str(n); return int(s + s[::-1])
print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Nov 02 2021

Formula

a(n) = n*10^A055642(n) + A004086(n).

a(n) = 11 * A066492(n).