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%I #11 Jan 27 2023 17:04:59
%S 1523,3251,7529,9257,154747,165857,171467,174767,312509,322519,373669,
%T 747451,758561,764171,767471,905213,915223,966373,1000033,1020233,
%U 1077733,1078733,1083833,1099933,1165643,1173743,1175743
%N Emirps (A006567) whose difference with the reversal is a perfect cube.
%C The differences are multiples of 1728.
%H Antonio Roldán, <a href="/A217387/b217387.txt">Table of n, a(n) for n = 1 to 40</a>
%e 905213 is prime, 312509 is prime. 905213 - 312509 = 592704 = 84^3.
%t Select[Prime[Range[100000]],!PalindromeQ[#]&&PrimeQ[IntegerReverse[#]] && IntegerQ[ CubeRoot[ Abs[#-IntegerReverse[#]]]]&] (* _Harvey P. Dale_, Jan 27 2023 *)
%o (PARI) isinteger(n)=(n==truncate(n))
%o reverse(n)=eval(concat(Vecrev(Str(n))))
%o 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) }
%o {for(i=2,10^7,p=reverse(i);if(isprime(i)&&isprime(p)&&iscube(abs(i-p)),print1(i," ")))} /* Antonio Roldán, Dec 19 2012 */
%K nonn,base
%O 1,1
%A _Antonio Roldán_, Oct 02 2012
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