cp's OEIS Frontend

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.

A188835 Decimal expansion of limit sqrt(1*sqrt(3*sqrt(5*sqrt(7*sqrt(9*...sqrt((2*n-1)...)))))).

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%I A188835 #17 Jun 02 2025 04:01:05
%S A188835 2,1,0,7,8,4,0,9,0,2,6,3,7,8,5,4,9,3,8,0,1,5,7,4,1,1,8,3,9,3,5,2,4,7,
%T A188835 0,2,9,7,1,6,9,5,8,3,5,7,4,6,5,9,3,4,5,8,2,8,0,9,4,7,0,5,3,6,0,3,2,6,
%U A188835 8,1,3,7,0,1,0,1,2,0,1,2,3,0,5,6,8,5,9,0,4,5,5,4,7,6,9,9,4,2,4,1
%N A188835 Decimal expansion of limit sqrt(1*sqrt(3*sqrt(5*sqrt(7*sqrt(9*...sqrt((2*n-1)...)))))).
%C A188835 A generalization of Somos quadratic recurrence constant A112302.
%H A188835 G. C. Greubel, <a href="/A188835/b188835.txt">Table of n, a(n) for n = 1..10000</a>
%F A188835 Product_{n>0} ((2*n + 1) / (2*n - 1)) ^ (2^-n). - _Michael Somos_, Feb 24 2014
%e A188835 2.10784090263785493...
%p A188835 with(numtheory);
%p A188835 P:=proc(i)
%p A188835 local a,n;
%p A188835 a:=1;
%p A188835 for n from i by -1 to 1 do a:=(2*n-1)*sqrt(a); od;
%p A188835 print(evalf(sqrt(a),1000));
%p A188835 end:
%p A188835 P(5000);
%t A188835 digits = 100; Clear[p]; p[m_] := p[m] = Fold[N[Sqrt[#2*#1], digits] &, 1, Range[2*m + 1, 1, -2]] // RealDigits[#, 10, digits] & // First; p[digits]; p[m = 2*digits]; While[p[m] != p[m/2], m = 2*m]; p[m] (* _Jean-François Alcover_, Feb 24 2014 *)
%Y A188835 Cf. A112302, A171759, A188834
%K A188835 nonn,cons
%O A188835 1,1
%A A188835 _Paolo P. Lava_, Apr 12 2011