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%I #9 Dec 31 2019 08:20:49
%S 1932,14592,122598,377370,2137548,16134048,18132978,34083432,43175478,
%T 46683060,64938702,126380340,145790430,163303200,326061120,328413078,
%U 385629198,413149992,483737628,526728990,659595048,675836598,871231200,919360920,931176330,938024028,996849108
%N Numbers k such that k, k + 2310, k + 2 * 2310, k + 3 * 2310, and k + 4 * 2310 are all averages of twin primes.
%e 1932 is a term since 1932, 1932 + 2310 = 4242, 1932 + 2 * 2310 = 6552, 1932 + 3 * 2310 = 8862, and 1932 + 4 * 2310 = 11172 are averages of twin primes.
%t q=2310; lst={}; Do[If[PrimeQ[n-1] &&PrimeQ[n+1] &&PrimeQ[n+q*1-1] &&PrimeQ[n+q*1+1] &&PrimeQ[n+q*2-1] &&PrimeQ[n+q*2+1] &&PrimeQ[n+q*3-1] &&PrimeQ[n+q*3+1] &&PrimeQ[n+q*4-1] &&PrimeQ[n+q*4+1], Print[n]; AppendTo[lst,n]], {n,10^8}];lst
%t Select[Range[4*10^5], And @@ PrimeQ[# + Plus @@@ Tuples[{{-1, 1}, 2310 * Range[0, 4]}]] &] (* _Amiram Eldar_, Dec 31 2019 *)
%Y Cf. A014574.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Aug 20 2008
%E More terms from _Amiram Eldar_, Dec 31 2019
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