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 A084764 #31 Jan 05 2025 19:51:37
%S A084764 1,4,31,1921,7380481,108942999582721,23737154316161495960243527681,
%T A084764 1126904990058528673830897031906808442930637286502826475521
%N A084764 a(n) = 2*a(n-1)^2 - 1, a(0)=1, a(1)=4.
%C A084764 Product_{k=1..n} (1 + 1/a(k)) converges to sqrt(5/3).
%C A084764 The next term has 115 digits. - _Harvey P. Dale_, Oct 31 2013
%H A084764 G. C. Greubel, <a href="/A084764/b084764.txt">Table of n, a(n) for n = 0..11</a>
%H A084764 H. S. Wilf, <a href="https://www.jstor.org/stable/2307914">Limit of a sequence, Elementary Problem E 1093</a>, Amer. Math. Monthly 61 (1954), 424-425.
%H A084764 Jeffrey Shallit, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/31-1/shallit.pdf">Rational numbers with non-terminating, non-periodic modified Engel-type expansions</a>, Fib. Quart., 31 (1993), 37-40.
%F A084764 With x=4+sqrt(15), y=4-sqrt(15): a(n+1) = (x^(2^n) + y^(2^n))/2.
%F A084764 a(n) = A005828(n-1), n>0. - _R. J. Mathar_, Sep 17 2008
%F A084764 a(n) = A001091(2^(n-1)) with a(0) = 1; i.e. a(n) = ChebyshevT(2^(n-1), 4) with a(0) = 1. - _G. C. Greubel_, May 16 2023
%t A084764 a[n_]:= a[n]= If[n<2, 4^n, 2 a[n-1]^2 -1]; Table[a[n], {n,0,10}]
%t A084764 Join[{1},NestList[2#^2-1&,4,10]] (* _Harvey P. Dale_, Oct 31 2013 *)
%o A084764 (Magma) [n le 2 select 4^(n-1) else 2*Self(n-1)^2 - 1: n in [1..10]]; // _G. C. Greubel_, May 16 2023
%o A084764 (SageMath)
%o A084764 def A084764(n): return 1 if n==0 else chebyshev_T(2^(n-1), 4)
%o A084764 [A084764(n) for n in range(11)] # _G. C. Greubel_, May 16 2023
%Y A084764 Cf. A001091, A005828 (essentially the same).
%K A084764 easy,nonn
%O A084764 0,2
%A A084764 Mario Catalani (mario.catalani(AT)unito.it), Jun 04 2003