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A132324 Decimal expansion of Product_{k>=1} (1+1/3^k). 3
1, 5, 6, 4, 9, 3, 4, 0, 1, 8, 5, 6, 7, 0, 1, 1, 5, 3, 7, 9, 3, 8, 8, 4, 9, 1, 0, 6, 7, 2, 8, 8, 3, 5, 4, 1, 6, 5, 6, 9, 4, 2, 5, 9, 1, 9, 8, 9, 5, 0, 3, 5, 0, 0, 9, 4, 9, 6, 7, 2, 1, 0, 2, 9, 9, 2, 3, 0, 2, 1, 1, 0, 7, 2, 5, 8, 0, 9, 6, 7, 6, 6, 9, 3, 9, 0, 3, 6, 6, 0, 3, 6, 7, 7, 2, 9, 6, 3, 8, 8, 1, 5, 2, 6, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Half the constant A132323.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1200

FORMULA

(1/2)*lim sup Product{k=0..floor(log_3(n)} (1+1/floor(n/3^k)) for n-->oo.

(1/2)*lim sup A132327(n)/A132027(n) for n-->oo.

(1/2)*lim sup A132327(n)/n^((1+log_3(n))/2) for n-->oo.

(1/2)*lim sup A132328(n)/n^((log_3(n)-1)/2) for n-->oo.

exp(Sum_{n>0} 3^(-n)*Sum_{k|n} -(-1)^k/k) = exp(Sum_{n>0} A000593(n)/(n*3^n)).

(1/2)*lim sup A132327(n+1)/A132327(n) = 1.56493401856701153793884910... for n-->oo.

Equals (-1/3; 1/3)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 01 2015

EXAMPLE

1.56493401856701153793884910...

MATHEMATICA

digits = 105; NProduct[1+1/3^k, {k, 1, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* Jean-Fran├žois Alcover, Feb 18 2014 *)

N[QPochhammer[-1/3, 1/3]] (* G. C. Greubel, Dec 01 2015 *)

CROSSREFS

Cf. A079555, A100220, A132019-A132026, A132034-A132038, A132265-A132268, A132323-A132326, A132327, A132328, A000593.

Sequence in context: A201678 A245870 A343063 * A021643 A021181 A082220

Adjacent sequences:  A132321 A132322 A132323 * A132325 A132326 A132327

KEYWORD

nonn,cons

AUTHOR

Hieronymus Fischer, Aug 20 2007

STATUS

approved

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Last modified June 18 16:47 EDT 2021. Contains 345120 sequences. (Running on oeis4.)