A342803 - OEIS

%I #69 Dec 23 2024 09:53:55

%S 67,449,1367,10303,12343,1003003,1022141,1230127,1234543,4004009,

%T 121200307,10022234347,10201204021,10203242527,12100242001,

%U 13310399303,16151080151,52281509069,61584539747,90608667517,104190107303,1020102040201,1022143262341,12384043938083

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

%C Palindromization is the function that minimally extends the string representation of a number into a palindrome (see A082216).

%C Are 13 and 1367 the unique terms leading to cubes or higher powers?

%C 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.

%C The next term (if it exists) is greater than 10^17.

%H Chai Wah Wu, <a href="/A342803/b342803.txt">Table of n, a(n) for n = 1..215</a>

%e The prime 449 belongs to sequence because 44944 is a square: 212^2.

%e The prime 1367 is in the sequence since 1367631 is a cube: 111^3.

%e 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

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

%Y Cf. A075786, A076443, A001597, A002113.

%Y Cf. A082216 (smallest palindrome beginning with n).

%Y Subsequence of primes of A342942.

%K nonn,base

%O 1,1

%A _Lamine Ngom_, Mar 22 2021

%E Corrected terms and missing terms added by _Chai Wah Wu_, Aug 26 2021