OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2000
FORMULA
lim inf (Product_{k=0..floor(log_12(n))} floor(n/12^k)*12^k/n) for n-->oo.
lim inf A132264(n)*12^((1+floor(log_12(n)))*floor(log_12(n))/2)/n^(1+floor(log_12(n))) for n-->oo.
(1/2)*exp(-Sum_{n>0} 12^(-n)*Sum_{k|n} 1/(k*2^k)).
Equals (1/2)*(1/24; 1/12)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 20 2015
EXAMPLE
0.47735217025489380198334286365820...
MATHEMATICA
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 *)
(1/2)*N[QPochhammer[1/24, 1/12], 200] (* G. C. Greubel, Dec 20 2015 *)
PROG
(PARI) prodinf(x=0, 1-1/(2*12^x)) \\ Altug Alkan, Dec 20 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hieronymus Fischer, Aug 20 2007
STATUS
approved