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 A075590 #15 Apr 17 2023 18:10:05
%S A075590 4,6,30,420,2310,43890,1138830,17160990,300690390,15651726090,
%T A075590 239378649510,12234189897930,461282657605770,19835154277048110,
%U A075590 693386350578511590,37508276737897976010,3338236629672919864890,209580878166809177658630,11465419967969569966774410
%N A075590 Smallest number with n distinct prime divisors which is the average of a twin prime pair.
%H A075590 T. D. Noe, <a href="/A075590/b075590.txt">Table of n, a(n) for n = 1..50</a>
%e A075590 a(4) = 420 = 2^2*3*5*7, (419,421) is a twin prime pair. (210 = 2*3*5*7, 211 is prime but 209 is composite).
%e A075590 a(8) = 17160990 = 2*3*5*7*11*17*19*23 and 17160989 = p[1100977], 17160991 = p[1100978].
%t A075590 t=Table[0, {10}]; Do[s=Length[FactorInteger[Prime[n]+1]]; If[PrimeQ[Prime[n]+2] && s<11 && t[[s]]==0, t[[s]]=Prime[n]+1], {n, 1, 1200000}]; t
%Y A075590 Cf. A014574, A068525, A294730.
%K A075590 nonn
%O A075590 1,1
%A A075590 _Amarnath Murthy_, Sep 26 2002
%E A075590 More terms from _Labos Elemer_, Sep 27 2002
%E A075590 Corrected and extended by _T. D. Noe_, Nov 30 2004. a(9)-a(18) were found by testing all the numbers x with n distinct prime factors, x < 3 prime(n)# and both x-1 and x+1 prime.