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A132038 Decimal expansion of Product_{k>0} (1-1/10^k). 32

%I

%S 8,9,0,0,1,0,0,9,9,9,9,8,9,9,9,0,0,0,0,0,0,1,0,0,0,0,9,9,9,9,9,9,9,9,

%T 8,9,9,9,9,9,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,9,9,9,9,9,9,9,9,9,9,9,

%U 9,8,9,9,9,9,9,9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,9,9,9

%N Decimal expansion of Product_{k>0} (1-1/10^k).

%H G. C. Greubel, <a href="/A132038/b132038.txt">Table of n, a(n) for n = 0..1500</a>

%H P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, 2009, page 49.

%F Equals exp( -Sum_{n>0} sigma_1(n)/(n*10^n) ).

%F Equals (1/10; 1/10)_{infinity}, where (a; q)_{infinity} is the q-Pochhammer symbol. - _G. C. Greubel_, Nov 30 2015

%e 0.8900100999989990000001000...

%t digits = 105; Clear[p]; p[n_] := p[n] = RealDigits[Product[1-1/10^k , {k, 1, n}], 10, digits] // First; p[10]; p[n=20]; While[p[n] != p[n/2], n = 2*n]; p[n] (* _Jean-Fran├žois Alcover_, Feb 17 2014 *)

%t RealDigits[QPochhammer[1/10], 10, 105][[1]] (* _Jean-Fran├žois Alcover_, Nov 18 2015 *)

%t N[Qpochhammer[1/10,1/10]] (* _G. C. Greubel_, Nov 30 2015 *)

%o (PARI) prodinf(x=1,-.1^x,1) \\ _Charles R Greathouse IV_, Nov 16 2013

%Y Cf. A000203, A027878, A048651, A067080, A098844, A100220, A132019, A132026.

%K nonn,cons

%O 0,1

%A _Hieronymus Fischer_, Aug 14 2007

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)