This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342803 #69 Dec 23 2024 09:53:55
%S A342803 67,449,1367,10303,12343,1003003,1022141,1230127,1234543,4004009,
%T A342803 121200307,10022234347,10201204021,10203242527,12100242001,
%U A342803 13310399303,16151080151,52281509069,61584539747,90608667517,104190107303,1020102040201,1022143262341,12384043938083
%N A342803 Primes p whose palindromization A082216(p) is a square or higher power.
%C A342803 Palindromization is the function that minimally extends the string representation of a number into a palindrome (see A082216).
%C A342803 Are 13 and 1367 the unique terms leading to cubes or higher powers?
%C A342803 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 A342803 The next term (if it exists) is greater than 10^17.
%H A342803 Chai Wah Wu, <a href="/A342803/b342803.txt">Table of n, a(n) for n = 1..215</a>
%e A342803 The prime 449 belongs to sequence because 44944 is a square: 212^2.
%e A342803 The prime 1367 is in the sequence since 1367631 is a cube: 111^3.
%e A342803 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 A342803 Select[Prime@Range@100000,Or@@(GCD@@Last/@FactorInteger@#>1&/@(FromDigits/@(Join[a,Reverse@#]&/@{a=IntegerDigits@#,Most@a})))&] (* _Giorgos Kalogeropoulos_, Mar 31 2021 *)
%Y A342803 Cf. A075786, A076443, A001597, A002113.
%Y A342803 Cf. A082216 (smallest palindrome beginning with n).
%Y A342803 Subsequence of primes of A342942.
%K A342803 nonn,base
%O A342803 1,1
%A A342803 _Lamine Ngom_, Mar 22 2021
%E A342803 Corrected terms and missing terms added by _Chai Wah Wu_, Aug 26 2021