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A154669 Averages k of twin prime pairs such that 2*k^3 + 12*k^2 is a square. 0

%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 k of twin prime pairs such that 2*k^3 + 12*k^2 is a square.

%C (11,13) is a twin prime pair with average 12; sqrt(2*12^3 + 12*12^2) = 72.

%p a := proc (n) if isprime(n-1) = 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); # _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[n-1]&&PrimeQ[n+1],AppendTo[lst,n]]],{n,9!}];lst

%t Select[Mean/@Select[Partition[Prime[Range[400000]],2,1],#[[2]]-#[[1]] == 2&],IntegerQ[Sqrt[2#^3+12#^2]]&] (* _Harvey P. Dale_, Sep 05 2017 *)

%Y Cf. A152811.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009

%E Extended by _Emeric Deutsch_, Jan 20 2009

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Last modified August 16 20:45 EDT 2022. Contains 356169 sequences. (Running on oeis4.)