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 A122579 #8 May 05 2025 10:09:17
%S A122579 1,1,3,15,455,53175,52802967,194817927511,3103080851583191,
%T A122579 200041552904055799767,52027813627693614618566103,
%U A122579 54341050032531342541499355961815
%N A122579 Integer sequence arising from the nested radical R(m) = sqrt(4^0+sqrt(4^1+sqrt(....+sqrt(4^m)...))) (see comment).
%C A122579 Let p(k) = Product_{i=0..k} (2^i+1) (A028361) then for any n>0 we get the asymptotic formula: lim_{m->oo} 2-R(m) = a(0)*(1/p(m))+a(1)*(2/p(m+1))+...+a(n)*(2^n/p(m+n))+O(1/p(m+n+1)). In particular there is this unexpected relation between an infinite nested radical and an infinite product: lim_{m->oo} (2-R(m))*2^(m*(m+1)/2) = 1/Product_{i>=0} (1+1/2^i) = 0.209... (A083864).
%D A122579 B. Cloitre, On an asymptotic formula for a nested radical, in preparation 2006
%F A122579 a(n) is asymptotic to c*4^(n*(n-1)/2) for c=0.041....
%Y A122579 Cf. A028361, A083864.
%K A122579 nonn,more
%O A122579 0,3
%A A122579 _Benoit Cloitre_, Oct 29 2006