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

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, 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, 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

Offset: 1

Author

Paolo P. Lava, Apr 12 2011

Keywords

• nonn
• cons

Comments

A generalization of Somos quadratic recurrence constant A112302.

Examples

			2.10784090263785493...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A112302, A171759, A188834

Programs

Maple

with(numtheory);
P:=proc(i)
local a,n;
a:=1;
for n from i by -1 to 1 do a:=(2*n-1)*sqrt(a); od;
print(evalf(sqrt(a),1000));
end:
P(5000);

Mathematica

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 *)

Formula

Product_{n>0} ((2*n + 1) / (2*n - 1)) ^ (2^-n). - Michael Somos, Feb 24 2014