A240453 - OEIS

%I #23 Dec 06 2021 16:21:14

%S 11,11,11,11,11,11,11,11,11,13,101,37,11,131,47,151,23,19,181,13,11,

%T 101,53,37,29,11,11,131,17,13,283,293,101,313,19,37,11,353,11,13,17,

%U 11,197,101,23,53,31,37,227,13,31,19,97,11,101,103,11,107,109,13

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

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

%C 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, ...

%H Michel Lagneau, <a href="/A240453/b240453.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p 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:

%t d[n_]:=IntegerDigits[n];Table[FactorInteger[FromDigits[Join[x=d[n],Reverse[x]]]][[-1,1]],{n,1,100}]

%t FactorInteger[#][[-1,1]]&/@Flatten[Table[Select[Range[10^n,10^(n+1)-1],PalindromeQ],{n,1,3,2}]] (* _Harvey P. Dale_, Dec 06 2021 *)

%o (Python)

%o from sympy import primefactors

%o def a(n): s = str(n); return max(primefactors(int(s + s[::-1])))

%o print([a(n) for n in range(1, 61)]) # _Michael S. Branicky_, Nov 11 2021

%Y Cf. A056524, A006530, A066492, A240454.

%K nonn,base,easy

%O 1,1

%A _Michel Lagneau_, Apr 05 2014