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A132020 Decimal expansion of product{k>=0, 1-1/(2*4^k)}. 4
4, 1, 9, 4, 2, 2, 4, 4, 1, 7, 9, 5, 1, 0, 7, 5, 9, 7, 7, 0, 9, 9, 5, 6, 1, 0, 7, 7, 0, 2, 9, 7, 4, 2, 5, 2, 2, 3, 3, 9, 5, 3, 2, 3, 4, 3, 9, 2, 6, 6, 6, 7, 4, 9, 0, 8, 0, 4, 4, 9, 9, 1, 6, 6, 3, 1, 7, 7, 2, 0, 5, 0, 8, 7, 2, 7, 0, 9, 1, 9, 3, 9, 1, 0, 0, 2, 3, 2, 4, 5, 4, 7, 4, 2, 3, 8, 1, 9, 5, 5, 0, 2, 8, 5, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also Product_k>0, 1-1/(2^k+1). - Robert G. Wilson v, May 25 2011

LINKS

Table of n, a(n) for n=0..104.

John E. Cremona and R. W. K. Odoni, Some density results for negative Pell equations; an application of graph theory, Journal of the London Mathematical Society s2-39:1 (1989), pp. 16-28.

FORMULA

lim inf product{0<=k<=floor(log_4(n)), floor(n/4^k)*4^k/n} for n-->oo.

lim inf A132028(n)/n^(1+floor(log_4(n)))*4^(1/2*(1+floor(log_4(n)))*floor(log_4(n))) for n-->oo.

lim inf A132028(n)/n^(1+floor(log_4(n)))*4^A000217(floor(log_4(n))) for n-->oo.

(1/2)*exp(-sum{n>0, 4^(-n)*sum{k|n, 1/(k*2^k))}}).

lim inf A132028(n)/A132028(n+1)=0.4194224417951075977... for n-->oo.

EXAMPLE

0.41942244179510759770995610770297425223395323439266674908044991663177...

MATHEMATICA

RealDigits[ Product[1 - 1/(2*4^i), {i, 0, 175}], 10, 111][[1]] (* Robert G. Wilson v, May 25 2011 *)

RealDigits[QPochhammer[1/2, 1/4], 10, 105][[1]] (* Jean-Fran├žois Alcover, Nov 18 2015 *)

PROG

(PARI) prodinf(k=0, 1-1.>>(2*k+1)) \\ Charles R Greathouse IV, Nov 16 2012

CROSSREFS

Cf. A048651, A098844, A067080, A132019, A132026, A132028, A100221, A000217.

Sequence in context: A085691 A055461 A104796 * A175643 A143864 A073364

Adjacent sequences:  A132017 A132018 A132019 * A132021 A132022 A132023

KEYWORD

nonn,cons

AUTHOR

Hieronymus Fischer, Aug 14 2007

EXTENSIONS

Name corrected by Charles R Greathouse IV, Nov 16 2012

STATUS

approved

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Last modified July 23 14:59 EDT 2017. Contains 289688 sequences.