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%I #6 Feb 04 2016 03:22:05
%S 432,4788,9000,211500,437472,564300,1231200,1232352,1271088,2368800,
%T 2609208,3042900,5523408,6773580,8560692,9604980,9985500,12797568,
%U 14653548,15630300,15850800,24770592,26462700,33242400,34716348
%N Averages of twin prime pairs of the form: sum of consecutive cubes.
%C 3^3+4^3+5^3+6^3=432, 9^3+10^3+11^3+12^3=4788,..
%H Chai Wah Wu, <a href="/A174717/b174717.txt">Table of n, a(n) for n = 1..10276</a>
%t mx=500;mz=mx^3+(mx+1)^3;lst={};Do[p=q^3;Do[p+=n^3;If[PrimeQ[p-1]&&PrimeQ[p+1],If[p>mz,Break[]];AppendTo[lst,p]],{n,q+1,mx+1}],{q,1,mx}];Union@lst
%Y Cf. A014574, A174716
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 27 2010
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