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%I #16 May 13 2013 01:49:39
%S 425783,263145359,744158711,1805712959,32484102023,103206118583,
%T 271979814143,324434645039,454854785303,626321908703,6944429711711,
%U 21648847849679,23586002145119
%N Primes of the form (n+1)^6+(n+2)^6+(n+3)^6-666.
%C Sum of three consecutive numbers with exponent 6, the difference with 666 generate prime number of the form 3n^6 +36n^5 +210n^4 +720n^3 +1470n^2 +1656n +128.
%e 425783 = 6^6+7^6+8^6-666 and 744158711 = 24^6+25^6+26^6-666 are in the sequence.
%t lst={};Do[If[PrimeQ[p=(n+1)^6+(n+2)^6+(n+3)^6-666],AppendTo[lst,p]],{n,200}];lst
%t Select[Total/@(Partition[Range[200],3,1]^6)-666,PrimeQ] (* _Harvey P. Dale_, Dec 14 2011 *)
%o (PARI) for(n=1,1e3,if(isprime(k=(n+1)^6+(n+2)^6+(n+3)^6-666),print1(k", "))) \\ _Charles R Greathouse IV_, Jul 01 2011
%K nonn
%O 1,1
%A _Rafael Parra Machio_, Jun 26 2011
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