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
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
Programs
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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
Comments