This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365201 #24 Sep 25 2023 07:29:05 %S A365201 74,146,194,218,302,482,586,734,746,842,914,1042,1138,1262,1346,1438, %T A365201 1574,1646,1654,1838,1874,1894,1906,1942,2026,2186,2206,2458,2462, %U A365201 2762,2906,2962,2974,3098,3106,3202,3218,3826,4198,4274,4286,4322,4414,4502,4534,4622,4666,4754,4934,4946 %N A365201 Even semiprimes that are the exact average of four consecutive odd semiprimes. %e A365201 74 is a term because (65 + 69 + 77 + 85)/4 = 74 = 2*37 is an even semiprime. %e A365201 218 is a term because (215 + 217 + 219 + 221)/4 = 218 = 2*109 is an even semiprime. %t A365201 sp=Select[Range[5,5200,2], PrimeOmega[#]==2&]; a={}; For[i=1, i<Length[sp]-3, i++, hav=Sum[Part[sp,k],{k,i,i+3}]/8; If[PrimeQ[hav], AppendTo[a,2hav]]]; a (* _Stefano Spezia_, Aug 25 2023 *) %o A365201 (PARI) upto(n) = {my(res = List(), l = List([0, 9, 15, 21]), s = sum(i = 1, #l, l[i]), i = l[#l]+2, ntimes4 = 4*n); while(1, if(bigomega(i) == 2, s += (i-l[1]); if(s > ntimes4, return(res)); if(s % 8 == 0 && isprime(s/8), listput(res, s/4)); listpop(l, 1); listput(l, i)); i+=2)} \\ _David A. Corneth_, Aug 26 2023 %Y A365201 Cf. A046315, A365200, A365202. %Y A365201 Subset of A100484. %K A365201 nonn %O A365201 1,1 %A A365201 _Elmo R. Oliveira_, Aug 25 2023