OFFSET
0,1
FORMULA
Equals lim inf_{n->oo} Product_{k=0..floor(log_10(n))} floor(n/10^k)*10^k/n.
Equals lim inf_{n->oo} A067080(n)/n^(1+floor(log_10(n)))*10^(1/2*(1+floor(log_10(n)))*floor(log_10(n))).
Equals 1/2*exp(-Sum_{n>0} 10^(-n)*Sum_{k|n} 1/(k*2^k)).
Equals Product_{n>=1} (1 - 1/A093136(n)). - Amiram Eldar, May 09 2023
EXAMPLE
0.472362443816572236551413383332...
MATHEMATICA
digits = 103; Product[1-1/(2*10^k), {k, 0, Infinity}] // N[#, digits+1]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
RealDigits[QPochhammer[1/2, 1/10], 10, 100][[1]] (* Jan Mangaldan, Jan 04 2017 *)
PROG
(PARI) prodinf(k=0, 1 - 1/(2*10^k)) \\ Amiram Eldar, May 09 2023
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hieronymus Fischer, Jul 28 2007
STATUS
approved