OFFSET
1,1
COMMENTS
From Jon E. Schoenfield, Jul 03 2023: (Start)
Equivalently, primes whose reversal is one less than the cube of a positive integer whose last digit is not a 1.
Since no prime starts or ends with a 0, reversing the prime will not change the number of digits, and since no prime consists only of 9's, adding 1 to its reversal will not change the number of digits, either, so the cube will have the same number of digits as the prime. Since the prime cannot begin with a 0, its reversal cannot end in 0, so the cube cannot end in 1 (and a cube ends in 1 if and only if its cube root ends in 1). Since cubes are less dense than primes, a reasonably efficient but simple way to search for all terms having at most D digits is to test each positive integer r < 10^(D/3) such that r mod 10 != 1: if the reversal of r^3 - 1 is a prime, then that prime is a term of the sequence. (End)
EXAMPLE
421 is prime and reversal(421) + 1 = 124 + 1 = 125 = 5^3.
364751 is in the sequence because it is prime and reversal(364751) + 1 = 157463 + 1 = 157464 = 54^3.
MATHEMATICA
Select[Prime@Range@1000000, IntegerQ@CubeRoot@(FromDigits@Reverse@IntegerDigits@#+1) &]
r = Select[Range@300, Mod[#, 3] != 1 && Mod[#, 10] != 1 &];
s = Sort@Select[FromDigits /@ Reverse /@ IntegerDigits@(r^3 - 1), PrimeQ]
PROG
(Python)
from sympy import isprime
s=[int(str(k**3-1)[::-1]) for k in range(1, 301)if k%10!=1 and k%3!=1]
t=[p for p in s if isprime(p)]
t.sort
print(t)
CROSSREFS
KEYWORD
base,nonn,easy
AUTHOR
Zhining Yang, Jul 03 2023
EXTENSIONS
a(18)-a(30) from Jon E. Schoenfield, Jul 03 2023
STATUS
approved