cp's OEIS Frontend

A132266 Decimal expansion of Product_{k>=0} (1 - 1/(2*12^k)).

%I A132266 #13 Dec 21 2015 03:32:59
%S A132266 4,7,7,3,5,2,1,7,0,2,5,4,8,9,3,8,0,1,9,8,3,3,4,2,8,6,3,6,5,8,2,0,2,3,
%T A132266 0,3,5,0,8,8,5,9,6,4,2,1,4,4,4,5,8,5,0,0,7,6,0,3,4,5,6,1,3,8,9,1,4,1,
%U A132266 2,8,8,8,5,7,9,1,6,3,5,2,4,7,7,2,8,0,9,4,1,6,5,3,5,3,6,1,1,3,5,0,0,3,7,2,5
%N A132266 Decimal expansion of Product_{k>=0} (1 - 1/(2*12^k)).
%H A132266 G. C. Greubel, <a href="/A132266/b132266.txt">Table of n, a(n) for n = 0..2000</a>
%F A132266 lim inf (Product_{k=0..floor(log_12(n))} floor(n/12^k)*12^k/n) for n-->oo.
%F A132266 lim inf A132264(n)*12^((1+floor(log_12(n)))*floor(log_12(n))/2)/n^(1+floor(log_12(n))) for n-->oo.
%F A132266 lim inf A132264(n)*12^A000217(floor(log_12(n)))/n^(1+floor(log_12(n))) for n-->oo.
%F A132266 (1/2)*exp(-Sum_{n>0} 12^(-n)*Sum_{k|n} 1/(k*2^k)).
%F A132266 lim inf A132264(n)/A132264(n+1) = 0.47735217025489380... for n-->oo.
%F A132266 Equals (1/2)*(1/24; 1/12)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - _G. C. Greubel_, Dec 20 2015
%e A132266 0.47735217025489380198334286365820...
%t A132266 digits = 105; NProduct[1-1/(2*12^k), {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%t A132266 (1/2)*N[QPochhammer[1/24, 1/12], 200] (* _G. C. Greubel_, Dec 20 2015 *)
%o A132266 (PARI) prodinf(x=0, 1-1/(2*12^x)) \\ _Altug Alkan_, Dec 20 2015
%Y A132266 Cf. A000217, A048651, A132019-A132026, A132034-A132038, A132265-A132268, A132323-A132326, A132264.
%K A132266 nonn,cons
%O A132266 0,1
%A A132266 _Hieronymus Fischer_, Aug 20 2007