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 A194427 #20 Aug 26 2025 15:55:53 %S A194427 1,3,8,13,21,47,65,99,143,209,214,227,233,234,244,260,277,283,297,328, %T A194427 353,399,409,431,451,509,516,533,543,671,675,677,701,737,741,748,767, %U A194427 786,795,804,854,856,890,937,981,986,992,994,1014,1080,1098,1129,1130,1160,1200,1213,1222,1227,1258 %N A194427 Indices k of twin prime averages A014574 which are two thirds of another twin prime average. %H A194427 Robert Israel, <a href="/A194427/b194427.txt">Table of n, a(n) for n = 1..2500</a> %e A194427 3 is in the sequence because A014574(3)=12 is two thirds of 18 and 18 is also a twin prime average. %p A194427 TPA:= 4: count:= 1: %p A194427 for p from 5 by 6 while count < 2000 do %p A194427 if isprime(p) and isprime(p+2) then count:= count+1; TPA:= TPA, p+1; fi %p A194427 od: %p A194427 TPA:= [TPA]: %p A194427 TPAS:= convert(TPA,set): %p A194427 T3:= map(`*`,TPAS,2/3) intersect TPAS: %p A194427 V:= Vector(nops(T3), proc(i) local k; member(T3[i],TPA,'k'); k end proc): %p A194427 convert(V,list); # _Robert Israel_, Aug 26 2025 %Y A194427 Cf. A014574. %K A194427 nonn,changed %O A194427 1,2 %A A194427 _Juri-Stepan Gerasimov_, Dec 02 2011