A217387 Emirps (A006567) whose difference with the reversal is a perfect cube.

1523, 3251, 7529, 9257, 154747, 165857, 171467, 174767, 312509, 322519, 373669, 747451, 758561, 764171, 767471, 905213, 915223, 966373, 1000033, 1020233, 1077733, 1078733, 1083833, 1099933, 1165643, 1173743, 1175743

Offset: 1

Author

Antonio Roldán, Oct 02 2012

Keywords

• nonn
• base

Comments

The differences are multiples of 1728.

Examples

			905213 is prime, 312509 is prime. 905213 - 312509 = 592704 = 84^3.
		

Links

• Antonio Roldán, Table of n, a(n) for n = 1 to 40

Programs

Mathematica

Select[Prime[Range[100000]],!PalindromeQ[#]&&PrimeQ[IntegerReverse[#]] && IntegerQ[ CubeRoot[ Abs[#-IntegerReverse[#]]]]&] (* Harvey P. Dale, Jan 27 2023 *)

PARI

isinteger(n)=(n==truncate(n))
reverse(n)=eval(concat(Vecrev(Str(n))))
iscube(n)= { local(f,m,p=0); if(n==1,p=1, f=factor(n); m=gcd(f[, 2]); if(isinteger(m/3),p=1));return(p) }
{for(i=2,10^7,p=reverse(i);if(isprime(i)&&isprime(p)&&iscube(abs(i-p)),print1(i," ")))} /* Antonio Roldán, Dec 19 2012 */