%I #24 Sep 25 2023 07:29:28
%S 146,194,302,478,482,614,706,1006,1438,1966,1994,2186,2206,2426,2462,
%T 2594,2614,3098,3274,3518,3742,3986,4282,4406,4594,4702,5354,5606,
%U 6038,6178,6218,6238,6442,6626,6782,7262,7642,7646,7886,8254,9098,9194,9298,9346,9442,9574,9938
%N Even semiprimes that are the exact average of six consecutive odd semiprimes.
%e 146 is a term because (133 + 141 + 143 + 145 + 155 + 159)/6 = 146 = 2*73 is an even semiprime.
%e 302 is a term because (295 + 299 + 301 + 303 + 305 + 309)/6 = 302 = 2*151 is an even semiprime.
%t sp=Select[Range[5,12000,2], PrimeOmega[#]==2&]; a={}; For[i=1, i<Length[sp]-5, i++, hav=Sum[Part[sp,k],{k,i,i+5}]/12; If[PrimeQ[hav], AppendTo[a,2hav]]]; a (* _Stefano Spezia_, Aug 25 2023 *)
%o (PARI) upto(n) = {my(res = List(), l = List([0,9,15,21,25,33]), s = sum(i = 1, #l, l[i]), i = l[#l]+2, ntimes6 = 6*n); while(1, if(bigomega(i) == 2, s += (i-l[1]); if(s > ntimes6, return(res)); if(s % 12 == 0 && isprime(s/12), listput(res, s/6)); listpop(l, 1); listput(l, i)); i+=2)} \\ _David A. Corneth_, Aug 26 2023
%Y Cf. A046315, A365200, A365201.
%Y Subset of A100484.
%K nonn
%O 1,1
%A _Elmo R. Oliveira_, Aug 25 2023