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A240453
Greatest prime divisors of the palindromes with an even number of digits.
3
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
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
KEYWORD
nonn,base,easy
AUTHOR
Michel Lagneau, Apr 05 2014
STATUS
approved