cp's OEIS Frontend

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.

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

This page as a plain text file.
%I A135067 #7 Aug 11 2024 14:41:34
%S A135067 8,343,1331,1030301
%N A135067 Palindromic cubes p^3, where p is a prime.
%C A135067 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 A135067 No further terms up to the 100,000th prime. - _Harvey P. Dale_, Jan 26 2021
%H A135067 P. De Geest, <a href="https://www.worldofnumbers.com/cube.htm">Palindromic Cubes</a>
%F A135067 a(n) = A135066(n)^3.
%e A135067 a(3) = 1331 because 11^3 = 1331 is a palindrome and 11 is a prime.
%t A135067 Do[ p = Prime[n]; f = p^3; If[ f == FromDigits[ Reverse[ IntegerDigits[ f ] ] ], Print[ {n, p, f} ]], {n, 1, 200000} ]
%t A135067 Select[Prime[Range[200]]^3,PalindromeQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 26 2021 *)
%Y A135067 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 A135067 more,nonn,base
%O A135067 1,1
%A A135067 _Alexander Adamchuk_, Nov 16 2007