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 A084717 #12 Jan 19 2023 03:12:32
%S A084717 3,6,12,24,48,192,384,1152,6912,27648,138240,691200,3456000,34560000,
%T A084717 138240000,414720000,2073600000,16588800000,364953600000,
%U A084717 4744396800000,66421555200000,132843110400000,664215552000000,3321077760000000,6642155520000000,132843110400000000
%N A084717 a(1) = 3 then a(n) = smallest multiple of a(n-1) > a(n-1) such that a(n) - 1 is a prime.
%H A084717 Amiram Eldar, <a href="/A084717/b084717.txt">Table of n, a(n) for n = 1..586</a>
%t A084717 a[1] = 3; a[n_] := a[n] = Catch[For[k = 2, True, k++, an = k*a[n - 1]; If[PrimeQ[an - 1], Throw[an]]]]; Table[a[n], {n, 1, 22}](* _Jean-François Alcover_, Nov 27 2012 *)
%t A084717 smp[n_]:=Module[{k=2},While[!PrimeQ[k*n-1],k++];k*n]; NestList[smp,3,30] (* _Harvey P. Dale_, Jun 03 2015 *)
%Y A084717 Cf. A084716, A084718, A036012.
%K A084717 nonn
%O A084717 1,1
%A A084717 _Amarnath Murthy_, Jun 11 2003
%E A084717 Edited by _Don Reble_, Jun 19 2003