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Palindromes with even number of digits.
15

%I #43 Nov 02 2021 11:00:59

%S 11,22,33,44,55,66,77,88,99,1001,1111,1221,1331,1441,1551,1661,1771,

%T 1881,1991,2002,2112,2222,2332,2442,2552,2662,2772,2882,2992,3003,

%U 3113,3223,3333,3443,3553,3663,3773,3883,3993,4004,4114,4224,4334,4444,4554

%N Palindromes with even number of digits.

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

%C A178788(a(n)) = 0 for n > 1. - _Reinhard Zumkeller_, Jun 30 2010

%C All of the terms are divisible by eleven. - _James Burling_, Aug 08 2014

%H Reinhard Zumkeller, <a href="/A056524/b056524.txt">Table of n, a(n) for n = 1..9999</a>

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

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

%t d[n_]:=IntegerDigits[n]; Table[FromDigits[Join[x=d[n],Reverse[x]]],{n,45}] (* _Jayanta Basu_, May 29 2013 *)

%t 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 *)

%o (Haskell)

%o a056524 n = a056524_list !! (n-1)

%o a056524_list = [read (ns ++ reverse ns) :: Integer |

%o n <- [0..], let ns = show n]

%o -- _Reinhard Zumkeller_, Dec 28 2011

%o (Python)

%o def a(n): s = str(n); return int(s + s[::-1])

%o print([a(n) for n in range(1, 46)]) # _Michael S. Branicky_, Nov 02 2021

%Y Cf. A002113, A004086, A056525, A066492.

%Y Cf. A020338, A055642, A178788.

%Y Cf. A110745 (permutation).

%K base,easy,nonn

%O 1,1

%A _Henry Bottomley_, Jun 16 2000