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%I #15 Apr 10 2018 14:37:36
%S 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 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 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 Decimal expansion of limit sqrt(1*sqrt(3*sqrt(5*sqrt(7*sqrt(9*...sqrt((2*n-1)...))))))
%C A generalization of Somos quadratic recurrence constant A112302.
%H G. C. Greubel, <a href="/A188835/b188835.txt">Table of n, a(n) for n = 1..10000</a>
%F Product_{n>0} ((2*n + 1) / (2*n - 1)) ^ (2^-n). - _Michael Somos_, Feb 24 2014
%e 2.10784090263785493...
%p with(numtheory);
%p P:=proc(i)
%p local a,n;
%p a:=1;
%p for n from i by -1 to 1 do a:=(2*n-1)*sqrt(a); od;
%p print(evalf(sqrt(a),1000));
%p end:
%p P(5000);
%t 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 Cf. A112302, A171759, A188834
%K nonn,cons
%O 1,1
%A _Paolo P. Lava_, Apr 12 2011
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