A048344 - OEIS

%I #23 Aug 11 2024 14:41:31

%S 12,21,102,112,122,201,211,221,1002,1011,1012,1021,1022,1101,1102,

%T 1112,1121,1201,1202,1211,2001,2011,2012,2021,2101,2102,2111,2201,

%U 10002,10011,10012,10021,10022,10102,10111,10112,10121,10202,10211,11001

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

%C Does any term in this sequence have any digit greater than 2? [From Harvey P. Dale, Nov 05 2011]

%H Reinhard Zumkeller, <a href="/A048344/b048344.txt">Table of n, a(n) for n = 1..1000</a>

%H P. De Geest, <a href="https://www.worldofnumbers.com/reversal.htm">Palindromic Products of Non Palindromic Integers and their Reversals </a>

%e E.g. 10021 x 12001 = 120262021 is a palindrome.

%t 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 *)

%t Select[Range[12000],!PalindromeQ[#]&&PalindromeQ[# IntegerReverse[#]]&] (* _Harvey P. Dale_, Jul 10 2023 *)

%o (Haskell)

%o a048344 n = a048344_list !! (n-1)

%o a048344_list = filter f a029742_list where

%o    f x = a136522 (x * a004086 x) == 1

%o -- _Reinhard Zumkeller_, Oct 09 2011

%o (Python)

%o A048344_list = []

%o for n in range(1,10**5):

%o ....s = str(n)

%o ....s2 = str(n)[::-1]

%o ....if s != s2:

%o ........s3 = str(n*int(s2))

%o ........if s3 == s3[::-1]:

%o ............A048344_list.append(n) # _Chai Wah Wu_, Sep 08 2014

%Y Cf. A048343.

%Y Cf. A004086, A136522, A029742.

%K nonn,base,nice

%O 1,1

%A _Patrick De Geest_, Feb 15 1999

%E Offset corrected by _Reinhard Zumkeller_, Oct 09 2011