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 A084737 #20 Feb 06 2024 19:31:06
%S A084737 1,2,4,10,40,250,2560,32590,543100,10242790,233335660,6703028890,
%T A084737 207263519020,7628001653830,311878265181040,13394639596851070,
%U A084737 628284422185342480,33217442899375387210,1955977793053588026280
%N A084737 Beginning with 1, numbers such that (a(n+2)-a(n+1))/(a(n+1)-a(n)) = prime(n).
%C A084737 Successive differences are primorials.
%H A084737 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A084737 From _Antti Karttunen_, Feb 06 2024: (Start)
%F A084737 For n >= 1, a(n) = A276085(2*A002110(n-1)).
%F A084737 For n >= 2, a(n) = 1 + A143293(n-2).
%F A084737 For n >= 3, a(n) = 2 + A060389(n-2).
%F A084737 (End)
%e A084737 a(3) = 4, a(4) = 10 and a(5) = 40 and (40-10)/(10-4) = 5 = prime(3).
%t A084737 Join[{1},Accumulate[FoldList[Times,1,Prime[Range[20]]]]+1] (* _Harvey P. Dale_, Dec 14 2011 *)
%Y A084737 Cf. A002110, A060389, A088860, A143293, A276085.
%K A084737 nonn
%O A084737 1,2
%A A084737 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 14 2003
%E A084737 More terms from _Vladeta Jovovic_, Jun 17 2003