%I #20 May 04 2016 19:21:33

%S 2267,2269,3527,3529,10331,10333,14867,14869,17207,17209,18521,18523,

%T 18917,18919,20231,20233,20357,20359,25577,25579,27791,27793,28547,

%U 28549,31247,31249,35279,35281,36899,36901,40697,40699,44279,44281,48779,48781,51479,51481

%N Twin primes both of which are the sum of three positive cubes.

%H Charles R Greathouse IV, <a href="/A272376/b272376.txt">Table of n, a(n) for n = 1..10000</a>

%e 3527 and 3529 are terms since 3527=3^3+5^3+15^3 and 3529=1^3+11^3+13^3.

%t cu[n_] := {}!=Quiet@ IntegerPartitions[n,{3},Range[n^(1/3)]^3, 1]; Flatten@ Rest@ Reap@ Do[If[ PrimeQ[p+2] && cu[p] && cu[p+2], Sow[{p, p+2}]], {p, Prime@ Range@ 10000}] (* _Giovanni Resta_, Apr 28 2016 *)

%o (PARI) list(lim)=my(v=List(), k, t); lim\=1; for(x=1, sqrtnint(lim-2, 3), for(y=1, min(sqrtnint(lim-x^3-1, 3), x), k=x^3+y^3; for(z=1, min(sqrtnint(lim-k, 3), y), if(isprime(t=k+z^3), listput(v, t))))); v=Set(v); for(i=2,#v-1,if(v[i]!=v[i-1]+2 && v[i]!=v[i+1]-2, v[i]=0)); v=Set(v); v[3..#v] \\ _Charles R Greathouse IV_, Apr 29 2016

%Y Cf. A001097, A007490, A270225.

%K nonn

%O 1,1

%A _Carmine Suriano_, Apr 28 2016