A135066 Primes p such that p^3 is a palindrome.

2, 7, 11, 101

Offset: 1

Author

Alexander Adamchuk, Nov 16 2007

Keywords

• nonn
• base
• more

Comments

Note that all first 4 listed terms are the palindromes. Corresponding palindromic cubes a(n)^3 are listed in A135067 = {8, 343, 1331, 1030301, ...}. PrimePi[ a(n) ] = {1, 4, 5, 26, ...}.

No further terms less than 1.29 * 10^10. - Michael S. Branicky, Feb 07 2021

Examples

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

Links

• Patrick De Geest, Palindromic Cubes

Crossrefs

Cf. A002780 (cube is a palindrome), A069748 (n and n^3 are both palindromes), A002781 (palindromic cubes), A135067 (palindromic cubes of primes).

Programs

Mathematica

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

Python

from sympy import nextprime
def ispal(n): s = str(n); return s == s[::-1]
p = 2
while True:
  if ispal(p**3): print(p)
  p = nextprime(p) # Michael S. Branicky, Feb 07 2021

Formula

a(n) = A135067(n)^(1/3).