This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A132323 #18 Aug 06 2024 05:06:03
%S A132323 3,1,2,9,8,6,8,0,3,7,1,3,4,0,2,3,0,7,5,8,7,7,6,9,8,2,1,3,4,5,7,6,7,0,
%T A132323 8,3,3,1,3,8,8,5,1,8,3,9,7,9,0,0,7,0,0,1,8,9,9,3,4,4,2,0,5,9,8,4,6,0,
%U A132323 4,2,2,1,4,5,1,6,1,9,3,5,3,3,8,7,8,0,7,3,2,0,7,3,5,4,5,9,2,7,7,6,3,0,5,2,0
%N A132323 Decimal expansion of Product_{k>=0} (1+1/3^k).
%C A132323 Twice the constant A132324.
%H A132323 G. C. Greubel, <a href="/A132323/b132323.txt">Table of n, a(n) for n = 1..1200</a>
%H A132323 Richard J. McIntosh, <a href="https://doi.org/10.1112/jlms/51.1.120">Some Asymptotic Formulae for q-Hypergeometric Series</a>, Journal of the London Mathematical Society, Vol. 51, No. 1 (1995), pp. 120-136; <a href="https://citeseerx.ist.psu.edu/pdf/4f03a5e304ec19f8a725774525aecd2a78f4ad81">alternative link</a>.
%F A132323 Equals lim sup_{n->oo} Product_{0<=k<=floor(log_3(n))} (1+1/floor(n/3^k)).
%F A132323 Equals lim sup_{n->oo} A132327(n)/A132027(n).
%F A132323 Equals lim sup_{n->oo} A132327(n)/n^((1+log_3(n))/2).
%F A132323 Equals lim sup_{n->oo} A132328(n)/n^((log_3(n)-1)/2).
%F A132323 Equals 2*exp(Sum_{n>0} 3^(-n) * Sum{k|n} -(-1)^k/k) = 2*exp(Sum_{n>0} A000593(n)/(n*3^n)).
%F A132323 Equals lim sup_{n->oo} A132327(n+1)/A132327(n).
%F A132323 Equals 2*(-1/3; 1/3)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - _G. C. Greubel_, Dec 01 2015
%F A132323 Equals sqrt(2) * exp(log(3)/24 + Pi^2/(12*log(3))) * Product_{k>=1} (1 - exp(-2*(2*k-1)*Pi^2/log(3))) (McIntosh, 1995). - _Amiram Eldar_, May 25 2023
%e A132323 3.12986803713402307587769821345767...
%t A132323 digits = 105; NProduct[1+1/3^k, {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%t A132323 2*N[QPochhammer[-1/3,1/3]] (* _G. C. Greubel_, Dec 01 2015 *)
%o A132323 (PARI) prodinf(x=0, 1+(1/3)^x) \\ _Altug Alkan_, Dec 03 2015
%Y A132323 Cf. A081845, A100220, A132019-A132026, A132034-A132038, A132265-A132268, A132324-A132326, A132327, A132328, A000593.
%K A132323 nonn,cons
%O A132323 1,1
%A A132323 _Hieronymus Fischer_, Aug 20 2007