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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A generalization of Somos quadratic recurrence constant A112302.

LINKS

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

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

Cf. A112302, A171759, A188834

Sequence in context: A327620 A325872 A021896 * A217735 A075615 A195284

Adjacent sequences: A188832 A188833 A188834 * A188836 A188837 A188838

KEYWORD

nonn,cons

AUTHOR

Paolo P. Lava, Apr 12 2011

STATUS

approved

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Last modified December 2 12:34 EST 2022. Contains 358496 sequences. (Running on oeis4.)