A240453 Greatest prime divisors of the palindromes with an even number of digits.

11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 101, 37, 11, 131, 47, 151, 23, 19, 181, 13, 11, 101, 53, 37, 29, 11, 11, 131, 17, 13, 283, 293, 101, 313, 19, 37, 11, 353, 11, 13, 17, 11, 197, 101, 23, 53, 31, 37, 227, 13, 31, 19, 97, 11, 101, 103, 11, 107, 109, 13

Offset: 1

Author

Michel Lagneau, Apr 05 2014

Keywords

• nonn
• base
• easy

Comments

Greatest prime divisor of A056524(n), or greatest prime divisor of the concatenation of a number n and reverse(n).

The palindromes with an even number of digits are composite numbers divisible by 11. There are many palindromic prime divisors, such as 11, 101, 131, 151, 181, 313, 353, ..., 30103, ...

Examples

			a(10) = 13 because the concatenation of 10 and 01 is 1001 = 7*11*13 where 13 is the greatest divisor of 1001.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056524, A006530, A066492, A240454.

Programs

Maple

with(numtheory):for n from 1 to 100 do:x:=convert(n,base,10):n1:=nops(x): s:=sum('x[i]*10^(n1-i)', 'i'=1..n1):y:=n*10^n1+s:z:=factorset(y):n2:=nops(z):d:=z[n2]:printf(`%d, `,d):od:

Mathematica

d[n_]:=IntegerDigits[n];Table[FactorInteger[FromDigits[Join[x=d[n],Reverse[x]]]][[-1,1]],{n,1,100}]
FactorInteger[#][[-1,1]]&/@Flatten[Table[Select[Range[10^n,10^(n+1)-1],PalindromeQ],{n,1,3,2}]] (* Harvey P. Dale, Dec 06 2021 *)

Python

from sympy import primefactors
def a(n): s = str(n); return max(primefactors(int(s + s[::-1])))
print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Nov 11 2021

Formula

a(n) = A006530(A056524(n)).