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A046447 Apart from initial term, composite numbers with the property that the concatenation of their prime factors is a palindrome.

%I A046447 #27 Apr 21 2025 13:22:37
%S A046447 1,4,8,9,16,25,27,32,39,49,64,69,81,119,121,125,128,129,159,219,243,
%T A046447 249,256,259,329,339,343,403,429,469,507,512,625,669,679,729,795,1024,
%U A046447 1207,1309,1329,1331,1533,1547,1587,1589,1703,2023,2048,2097,2187,2319
%N A046447 Apart from initial term, composite numbers with the property that the concatenation of their prime factors is a palindrome.
%C A046447 Prime factors considered with multiplicity. - _Harvey P. Dale_, Apr 20 2025
%H A046447 Reinhard Zumkeller, <a href="/A046447/b046447.txt">Table of n, a(n) for n = 1..1000</a>
%e A046447 81 is a term because 81 = 3 * 3 * 3 * 3 -> 3333 is palindromic.
%t A046447 concat[n_]:=Flatten[Table[IntegerDigits[First[n]],{Last[n]}]]; palQ[n_]:= Module[{x=Flatten[concat/@FactorInteger[n]]},x==Reverse[x]&&!PrimeQ[n]]; Select[Range[2500],palQ] (* _Harvey P. Dale_, May 24 2011 *)
%t A046447 cpfpQ[n_]:=PalindromeQ[FromDigits[Flatten[IntegerDigits/@Flatten[PadRight[{},#[[2]],#[[1]]]&/@FactorInteger[n]]]]]; Join[{1},Select[Range[2500],CompositeQ[ #]&&cpfpQ[#]&]] (* _Harvey P. Dale_, Apr 20 2025 *)
%o A046447 (Haskell)
%o A046447 a046447 n = a046447_list !! (n-1)
%o A046447 a046447_list = 1 : filter f [1..] where
%o A046447    f x = length ps > 1 && ps' == reverse ps'
%o A046447          where ps' = concatMap show ps; ps = a027746_row x
%o A046447 -- _Reinhard Zumkeller_, May 02 2014
%o A046447 (Python)
%o A046447 from sympy import factorint, isprime
%o A046447 A046447_list = [1]
%o A046447 for n in range(4, 10**6):
%o A046447     if not isprime(n):
%o A046447         s = ''.join([str(p)*e for p, e in sorted(factorint(n).items())])
%o A046447         if s == s[::-1]:
%o A046447             A046447_list.append(n) # _Chai Wah Wu_, Jan 03 2015
%Y A046447 Cf. A046448, A046449, A046450.
%Y A046447 Cf. A027746, A018252, A136522, A002113.
%K A046447 nonn,nice,base
%O A046447 1,2
%A A046447 _Patrick De Geest_, Jul 15 1998
%E A046447 Definition slightly modified by _Harvey P. Dale_, Apr 20 2025