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 A117805 #26 Oct 11 2023 15:17:03
%S A117805 3,6,30,870,756030,571580604870,326704387862983487112030,
%T A117805 106735757048926752040856495274871386126283608870,
%U A117805 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068030
%N A117805 Start with 3. Square the previous term and subtract it.
%C A117805 The next term is too large to include.
%C A117805 a(n) = A005267(n+1)+1. - _R. J. Mathar_, Apr 22 2007. This is true by induction. - _M. F. Hasler_, May 04 2007<
%C A117805 For any a(0) > 2, the sequence a(n) = a(n-1) * (a(n-1) - 1) gives a constructive proof that there exists integers with at least n + 1 distinct prime factors, e.g., a(n). As a corollary, this gives a constructive proof of Euclid's theorem stating that there are an infinity of primes. - _Daniel Forgues_, Mar 03 2017
%F A117805 a(0) = 3, a(n) = (a(n-1))^2 - a(n-1).
%F A117805 a(n) ~ c^(2^n), where c = 2.330283023986140936420341573975137247354077600883596774023675490739568138... . - _Vaclav Kotesovec_, Dec 17 2014
%e A117805 Start with 3; 3^2 - 3 = 6; 6^2 - 6 = 30; etc.
%p A117805 f:=proc(n) option remember; if n=0 then RETURN(3); else RETURN(f(n-1)^2-f(n-1)); fi; end;
%t A117805 k=3;lst={k};Do[k=k^2-k;AppendTo[lst,k],{n,9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2010 *)
%t A117805 RecurrenceTable[{a[0]==3, a[n]==a[n-1]*(a[n-1] - 1)}, a, {n, 0, 10}] (* _Vaclav Kotesovec_, Dec 17 2014 *)
%t A117805 NestList[#^2-#&,3,10] (* _Harvey P. Dale_, Oct 11 2023 *)
%Y A117805 Cf. A007018.
%K A117805 easy,nonn
%O A117805 0,1
%A A117805 _Jacob Vecht_, Apr 29 2006