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 A078570 #14 Jul 31 2023 15:48:50 %S A078570 1,2,2,2,3,3,3,2,3,2,3,3,3,2,3,3,3,3,3,3,3,4,2,4,3,4,3,3,3,4,3,3,3,4, %T A078570 3,4,3,4,3,4,2,4,3,4,4,4,4,3,4,3,3,3,3,3,4,3,3,3,4,4,3,3,3,3,3,4,4,3, %U A078570 3,5,4,3,4,2,3,3,3,5,4,3,4,3,4,3,3,3,4,4,4,3,4,3,3,3,4,3,3,3,3,4,3,3,4,4,4 %N A078570 Number of distinct prime factors of the average of n-th twin prime pair. %H A078570 Amiram Eldar, <a href="/A078570/b078570.txt">Table of n, a(n) for n = 1..10000</a> %F A078570 a(n) = A001221(A014574(n)). %e A078570 12th twin prime pair = (A001359(12), A006512(12)) = (149,151), hence A014574(12) = 150 = 2*3*5*5, therefore a(12) = 3. %t A078570 midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; PrimeNu /@ Select[Range[5000], midQ] (* _Amiram Eldar_, Nov 03 2019 *) %t A078570 PrimeNu[Mean[#]]&/@Select[Partition[Prime[Range[1000]],2,1],#[[2]]-#[[1]]==2&] (* _Harvey P. Dale_, Jul 31 2023 *) %Y A078570 Cf. A001221, A014574, A078571, A078572. %K A078570 nonn %O A078570 1,2 %A A078570 _Reinhard Zumkeller_, Nov 29 2002