OFFSET
1,1
COMMENTS
Palindromization is the function that minimally extends the string representation of a number into a palindrome (see A082216).
Are 13 and 1367 the unique terms leading to cubes or higher powers?
It seems that 13 is the unique prime whose even palindromization (the concatenation of a number and its reversal) is a square or higher power).
The next term (if it exists) is greater than 10^17.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..215
EXAMPLE
The prime 449 belongs to sequence because 44944 is a square: 212^2.
The prime 1367 is in the sequence since 1367631 is a cube: 111^3.
The prime 13 is not a term as A082216(13) = 131 and 131 is prime. The prime 10303 is in the sequence since 1030301 is a cube: 101^3. - Chai Wah Wu, Aug 26 2021
MATHEMATICA
Select[Prime@Range@100000, Or@@(GCD@@Last/@FactorInteger@#>1&/@(FromDigits/@(Join[a, Reverse@#]&/@{a=IntegerDigits@#, Most@a})))&] (* Giorgos Kalogeropoulos, Mar 31 2021 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Lamine Ngom, Mar 22 2021
EXTENSIONS
Corrected terms and missing terms added by Chai Wah Wu, Aug 26 2021
STATUS
approved