A072384 Primes which can be represented as the sum of a cube and its reverse.

2, 727, 79697, 85147, 100699, 3946493, 9715169, 10301029, 11592961, 11851481, 13888793, 13913093, 17746387, 125000521, 176232571, 358030753, 417302813, 433748423, 726463627, 810090007, 817807817, 832595227, 854121557, 875444677

Offset: 1

Author

Shyam Sunder Gupta, Jul 20 2002

Keywords

• base
• nonn

Examples

			727 is a term because it is prime and it is the sum of cube 512 and its reverse 215.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000 (corrected by Sean A. Irvine)

Crossrefs

Cf. A000578, A004086, A004165, A319603.

Programs

Mathematica

Select[#+IntegerReverse[#]&/@(Range[1000]^3),PrimeQ]//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2016 *)

Python

from sympy import isprime
def rev(n): return int(str(n)[::-1])
def aupto(lim):
    c = [p**3 for p in range(1, int(lim**(1/3))+2)]
    s = set(ara for ara in (a + rev(a) for a in c) if ara <= lim)
    return sorted(filter(isprime, s))
print(aupto(10**9)) # Michael S. Branicky, Jun 26 2021