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

1,1

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.

Cf. A110745 (permutation).

Sequence in context: A240927 A272655 A333440 * A110745 A280826 A020338

Adjacent sequences: A056521 A056522 A056523 * A056525 A056526 A056527

Keyword

base,easy,nonn

Author

Henry Bottomley, Jun 16 2000

Status

approved