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

1,1

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, ...

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A056524, A006530, A066492, A240454.

Sequence in context: A317244 A113587 A083971 * A052192 A110733 A090862

Adjacent sequences: A240450 A240451 A240452 * A240454 A240455 A240456

Keyword

nonn,base,easy

Author

Michel Lagneau, Apr 05 2014

Status

approved