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A188835
Decimal expansion of limit sqrt(1*sqrt(3*sqrt(5*sqrt(7*sqrt(9*...sqrt((2*n-1)...))))))
4
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
1,1
COMMENTS
A generalization of Somos quadratic recurrence constant A112302.
LINKS
FORMULA
Product_{n>0} ((2*n + 1) / (2*n - 1)) ^ (2^-n). - Michael Somos, Feb 24 2014
EXAMPLE
2.10784090263785493...
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 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, Apr 12 2011
STATUS
approved