A135067 Palindromic cubes p^3, where p is a prime.

8, 343, 1331, 1030301

Offset: 1

Author

Alexander Adamchuk, Nov 16 2007

Keywords

• more
• nonn
• base

Comments

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, ...}.

No further terms up to the 100,000th prime. - Harvey P. Dale, Jan 26 2021

Examples

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

Links

• P. De Geest, Palindromic Cubes

Crossrefs

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.

Programs

Mathematica

Do[ p = Prime[n]; f = p^3; If[ f == FromDigits[ Reverse[ IntegerDigits[ f ] ] ], Print[ {n, p, f} ]], {n, 1, 200000} ]
Select[Prime[Range[200]]^3,PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 26 2021 *)

Formula

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