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A270244 Lesser of twin primes such that the sum of the twin prime pair is the sum of 2 positive cubes.

%I A270244 #14 Mar 17 2016 05:59:36
%S A270244 1871,8819,74609,77237,81647,93131,98927,102059,108107,110501,152837,
%T A270244 180287,220859,241919,256031,275939,309851,319679,422099,457001,
%U A270244 459647,462419,490247,530711,568151,635291,660851,667547,721619,729269,761669,843677,859679,909971,948401,1037087,1041119
%N A270244 Lesser of twin primes such that the sum of the twin prime pair is the sum of 2 positive cubes.
%H A270244 Chai Wah Wu, <a href="/A270244/b270244.txt">Table of n, a(n) for n = 1..10000</a>
%e A270244 1871 is a term because 1871 + 1873 = 10^3 + 14^3.
%e A270244 8819 is a term because 8819 + 8821 = 4^3 + 26^3.
%e A270244 74609 is a term because 74609 + 74611 = 7^3 + 53^3.
%t A270244 Select[Select[Prime@ Range[10^5], PrimeQ[# + 2] &], Length[PowersRepresentations[2 # + 2, 2, 3] /. {0, _} -> Nothing] > 0 &] (* _Michael De Vlieger_, Mar 15 2016 *)
%o A270244 (PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
%o A270244 t(n,p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
%o A270244 for(n=1, 1e4, if(isA003325(2*t(n)+2), print1(t(n), ", ")));
%Y A270244 Cf. A001359, A003325, A054735.
%K A270244 nonn
%O A270244 1,1
%A A270244 _Altug Alkan_, Mar 13 2016