A056525 Palindromes with odd number of digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515, 525, 535, 545, 555, 565

Offset: 1

Author

Henry Bottomley, Jun 16 2000

Keywords

• base
• easy
• nonn

Comments

Concatenation of all but final digits of n with reverse of n (keeping leading zeros in the reverse)

A178788(a(n)) = 0 for n > 9. [From Reinhard Zumkeller, Jun 30 2010]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A002113, A004086, A056524.

Programs

Haskell

a056525 n = a056525_list !! (n-1)
a056525_list = [1..9] ++ [read (ns ++ [z] ++ reverse ns) |
                n <- [1..], let ns = show n, z <- "0123456789"]
-- Reinhard Zumkeller, Dec 28 2011

Mathematica

Join[Range[9],Table[FromDigits[Join[x=IntegerDigits[n],Reverse[Drop[x,-1]]]],{n,10,56}]] (* Jayanta Basu, May 29 2013 *)
Select[Flatten[Table[Range[10^n,10^(n+1)-1],{n,0,2,2}]],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 21 2020 *)

Formula

a(n) = floor[n/10]*10^A055642(n)+A004086(n)