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Palindromic cubes p^3, where p is a prime.
1

%I #7 Aug 11 2024 14:41:34

%S 8,343,1331,1030301

%N Palindromic cubes p^3, where p is a prime.

%C Corresponding primes p such that a(n) = p^3 are listed in A135066 = {2, 7, 11, 101, ...} = Primes p such that p^3 is a palindrome. PrimePi[ a(n)^(1/3) ] = {1, 4, 5, 26, ...}.

%C No further terms up to the 100,000th prime. - _Harvey P. Dale_, Jan 26 2021

%H P. De Geest, <a href="https://www.worldofnumbers.com/cube.htm">Palindromic Cubes</a>

%F a(n) = A135066(n)^3.

%e a(3) = 1331 because 11^3 = 1331 is a palindrome and 11 is a prime.

%t Do[ p = Prime[n]; f = p^3; If[ f == FromDigits[ Reverse[ IntegerDigits[ f ] ] ], Print[ {n, p, f} ]], {n, 1, 200000} ]

%t Select[Prime[Range[200]]^3,PalindromeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 26 2021 *)

%Y Cf. A002780 = Cube is a palindrome. Cf. A069748 = Numbers n such that n and n^3 are both palindromes. Cf. A002781 = Palindromic cubes. Cf. A135066 = Primes p such that p^3 is a palindrome.

%K more,nonn,base

%O 1,1

%A _Alexander Adamchuk_, Nov 16 2007