A048344 a(n) * a(n)_reversed is a palindrome (and a(n) is not palindromic).

12, 21, 102, 112, 122, 201, 211, 221, 1002, 1011, 1012, 1021, 1022, 1101, 1102, 1112, 1121, 1201, 1202, 1211, 2001, 2011, 2012, 2021, 2101, 2102, 2111, 2201, 10002, 10011, 10012, 10021, 10022, 10102, 10111, 10112, 10121, 10202, 10211, 11001

Offset: 1

Author

Patrick De Geest, Feb 15 1999

Keywords

• nonn
• base
• nice
• changed

Comments

Does any term in this sequence have any digit greater than 2? - Harvey P. Dale, Nov 05 2011

Examples

			E.g. 10021 * 12001 = 120262021 is a palindrome.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Patrick De Geest, Palindromic Products of Non Palindromic Integers and their Reversals

Crossrefs

Cf. A048343.

Cf. A004086, A136522, A029742.

Programs

Haskell

a048344 n = a048344_list !! (n-1)
a048344_list = filter f a029742_list where
   f x = a136522 (x * a004086 x) == 1
-- Reinhard Zumkeller, Oct 09 2011

Mathematica

palQ[n_]:=Module[{idn=IntegerDigits[n],ridn,idn2},ridn=Reverse[idn]; idn2 = IntegerDigits[ n FromDigits[ridn]];idn!=ridn&&idn2==Reverse[idn2]]; Select[ Range[11100],palQ] (* Harvey P. Dale, Nov 05 2011 *)
Select[Range[12000],!PalindromeQ[#]&&PalindromeQ[# IntegerReverse[#]]&] (* Harvey P. Dale, Jul 10 2023 *)

Python

A048344_list = []
for n in range(1,10**5):
    s = str(n)
    s2 = str(n)[::-1]
    if s != s2:
        s3 = str(n*int(s2))
        if s3 == s3[::-1]:
            A048344_list.append(n) # Chai Wah Wu, Sep 08 2014

Extensions

Offset corrected by Reinhard Zumkeller, Oct 09 2011