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%I #8 May 13 2022 17:15:47
%S 7,75,178,209,371,431,497,516,679,770,802,830,858,931,957,1221,1232,
%T 1251,1309,1397,1419,1545,1567,1683,1713,1714,1834,1901,1991,2337,
%U 2408,2441,2505,2623,2651,2673,2726,3142,3223,3269,3349,3386,3387,3461,3492
%N Least of 5 consecutive integers such that their product is the average of a twin prime pair.
%C 7*8*9*10*11=55440 +-1 -> primes,..
%H Harvey P. Dale, <a href="/A174243/b174243.txt">Table of n, a(n) for n = 1..1000</a>
%t f1[n_]:=PrimeQ[n-1]&&PrimeQ[n+1];f2[n_]:=n*(n+1)*(n+2)*(n+3)*(n+4);lst={};Do[If[f1[f2[n]],AppendTo[lst,n]],{n,8!}];lst
%t Select[Partition[Range[3500],5,1],AllTrue[Times@@#+{1,-1},PrimeQ]&][[All,1]] (* _Harvey P. Dale_, May 13 2022 *)
%Y Cf. A014574, A174242
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 13 2010
%E Definition modified by _Harvey P. Dale_, May 13 2022
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