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

1, 4, 8, 9, 16, 25, 27, 32, 39, 49, 64, 69, 81, 119, 121, 125, 128, 129, 159, 219, 243, 249, 256, 259, 329, 339, 343, 403, 429, 469, 507, 512, 625, 669, 679, 729, 795, 1024, 1207, 1309, 1329, 1331, 1533, 1547, 1587, 1589, 1703, 2023, 2048, 2097, 2187, 2319

Offset: 1

Author

Patrick De Geest, Jul 15 1998

Keywords

• nonn
• nice
• base

Comments

Prime factors considered with multiplicity. - Harvey P. Dale, Apr 20 2025

Examples

			81 is a term because 81 = 3 * 3 * 3 * 3 -> 3333 is palindromic.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046448, A046449, A046450.

Cf. A027746, A018252, A136522, A002113.

Programs

Haskell

a046447 n = a046447_list !! (n-1)
a046447_list = 1 : filter f [1..] where
   f x = length ps > 1 && ps' == reverse ps'
         where ps' = concatMap show ps; ps = a027746_row x
-- Reinhard Zumkeller, May 02 2014

Mathematica

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 *)
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 *)

Python

from sympy import factorint, isprime
A046447_list = [1]
for n in range(4, 10**6):
    if not isprime(n):
        s = ''.join([str(p)*e for p, e in sorted(factorint(n).items())])
        if s == s[::-1]:
            A046447_list.append(n) # Chai Wah Wu, Jan 03 2015

Extensions

Definition slightly modified by Harvey P. Dale, Apr 20 2025