OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1500
Eric Weisstein's World of Mathematics, q-Pochhammer Symbol
FORMULA
lim inf Product_{k=0..floor(log_11(n))} floor(n/11^k)*11^k/n for n-->oo.
lim inf A132263(n)*11^((1+floor(log_11(n)))*floor(log_11(n))/2)/n^(1+floor(log_11(n))) for n-->oo.
(1/2)*exp(-Sum_{n>0} 11^(-n)*Sum_{k|n} 1/(k*2^k)).
Equals (1/2; 1/11)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Nov 30 2015
EXAMPLE
0.47510412750760310539756444...
MATHEMATICA
digits = 105; NProduct[1-1/(2*11^k), {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+10] // N[#, digits+10]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
N[QPochhammer[1/2, 1/11]] (* G. C. Greubel, Nov 30 2015 *)
PROG
(PARI) prodinf(x=0, 1 - 1/(2*11^x)) \\ Altug Alkan, Dec 01 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hieronymus Fischer, Aug 20 2007
STATUS
approved