A056524 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

FORMULA

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

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

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 *)

PROG

(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

(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

CROSSREFS

Cf. A002113, A004086, A056525, A066492.

Cf. A020338, A055642, A178788.