A342803 Primes p whose palindromization A082216(p) is a square or higher power.

67, 449, 1367, 10303, 12343, 1003003, 1022141, 1230127, 1234543, 4004009, 121200307, 10022234347, 10201204021, 10203242527, 12100242001, 13310399303, 16151080151, 52281509069, 61584539747, 90608667517, 104190107303, 1020102040201, 1022143262341, 12384043938083

Offset: 1

Author

Lamine Ngom, Mar 22 2021

Keywords

• nonn
• base

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.

Examples

			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
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..215

Crossrefs

Cf. A075786, A076443, A001597, A002113.

Cf. A082216 (smallest palindrome beginning with n).

Subsequence of primes of A342942.

Programs

Mathematica

Select[Prime@Range@100000,Or@@(GCD@@Last/@FactorInteger@#>1&/@(FromDigits/@(Join[a,Reverse@#]&/@{a=IntegerDigits@#,Most@a})))&] (* Giorgos Kalogeropoulos, Mar 31 2021 *)

Extensions

Corrected terms and missing terms added by Chai Wah Wu, Aug 26 2021