OFFSET
0,1
FORMULA
Equals lim inf_{n->oo} Product_{k=0..floor(log_9(n))} floor(n/9^k)*9^k/n.
Equals lim inf_{n->oo} A132033(n)/n^(1+floor(log_9(n)))*9^(1/2*(1+floor(log_9(n)))*floor(log_9(n))).
Equals (1/2)*exp(-Sum_{n>0} 9^(-n)*Sum_{k|n} 1/(k*2^k)).
Equals Product_{n>=1} (1 - 1/A270369(n)). - Amiram Eldar, May 08 2023
EXAMPLE
0.4689451783670236932832800...
MATHEMATICA
digits = 103; NProduct[1-1/(2*9^k), {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
RealDigits[QPochhammer[1/2, 1/9], 10, 120][[1]] (* Amiram Eldar, May 08 2023 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hieronymus Fischer, Aug 14 2007
STATUS
approved