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.

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

Original entry on oeis.org

2, 7, 11, 101
Offset: 1

Views

Author

Alexander Adamchuk, Nov 16 2007

Keywords

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

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).
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