OFFSET
1,1
COMMENTS
(11,13) is a twin prime pair with average 12; sqrt(2*12^3 + 12*12^2) = 72.
MAPLE
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
MATHEMATICA
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
Select[Mean/@Select[Partition[Prime[Range[400000]], 2, 1], #[[2]]-#[[1]] == 2&], IntegerQ[Sqrt[2#^3+12#^2]]&] (* Harvey P. Dale, Sep 05 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jan 13 2009
EXTENSIONS
Extended by Emeric Deutsch, Jan 20 2009
STATUS
approved