login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A317244 A113587 A083971 * A052192 A110733 A090862
KEYWORD
nonn,base,easy
AUTHOR
Michel Lagneau, Apr 05 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)