%I
%S 12,282,642,1452,12162,17292,34842,98562,194682,233922,347772,383682,
%T 410412,544962,749082,1071642,1302492,1421292,1503372,1685442,2794242,
%U 3011052,3235962,3312732,3792252,3875322,4755522
%N Averages of twin prime pairs n such that 2*n^3+12*n^2 is a square.
%C 11,12,13;Sqrt[2*12^3+12*12^2]=72,...
%p a := proc (n) if isprime(n1) = true and isprime(n+1) = true and type(sqrt(2*n^3+12*n^2), integer) = true then n else end if end proc: seq(a(n), n = 3 .. 5000000); [From _Emeric Deutsch_, Jan 20 2009]
%t a[n_]:=Sqrt[2*n^3+12*n^2];lst={};Do[If[Floor[a[n]]==a[n],If[PrimeQ[n1]&&PrimeQ[n+1],AppendTo[lst,n]]],{n,9!}];lst
%Y Cf. A152811
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009
%E Extended by _Emeric Deutsch_, Jan 20 2009
