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A132038 Decimal expansion of Product_{k>0} (1-1/10^k). 32
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1500

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009, page 49.

FORMULA

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

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

EXAMPLE

0.8900100999989990000001000...

MATHEMATICA

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-François Alcover, Feb 17 2014 *)

RealDigits[QPochhammer[1/10], 10, 105][[1]] (* Jean-François Alcover, Nov 18 2015 *)

N[Qpochhammer[1/10, 1/10]] (* G. C. Greubel, Nov 30 2015 *)

PROG

(PARI) prodinf(x=1, -.1^x, 1) \\ Charles R Greathouse IV, Nov 16 2013

CROSSREFS

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

Sequence in context: A078247 A273555 A213153 * A087495 A111253 A021533

Adjacent sequences:  A132035 A132036 A132037 * A132039 A132040 A132041

KEYWORD

nonn,cons

AUTHOR

Hieronymus Fischer, Aug 14 2007

STATUS

approved

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Last modified June 22 23:15 EDT 2017. Contains 288633 sequences.