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Numbers n such that n!!! is an interprime.
1

%I #5 Aug 02 2018 19:31:35

%S 4,6,13,15,16,23,28,46,126,148,285

%N Numbers n such that n!!! is an interprime.

%C No additional terms up to n = 700. - _Harvey P. Dale_, Aug 02 2018

%t PrevPrim[n_] := Block[{k = n - 1}, While[ ! PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; NFactorialM[n_, m_] := Block[{k = n, p = n}, While[k > m, k -= m; p = p*k]; p]; Do[ a = NFactorialM[n, 3]; If[2a == PrevPrim[a] + NextPrim[a], Print[n]], {n, 3, 500}]

%t npipQ[n_]:=Module[{p=Times@@Range[n,1,-3]},p==Mean[{NextPrime[ p], NextPrime[ p,-1]}]]; Select[Range[300],npipQ] (* _Harvey P. Dale_, Aug 02 2018 *)

%Y Cf. A053709 & A074176.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 16 2002