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A132022
Decimal expansion of Product_{k>=0} (1 - 1/(2*6^k)).
4
4, 5, 0, 7, 1, 2, 6, 2, 5, 2, 2, 6, 0, 3, 9, 1, 3, 0, 8, 3, 0, 0, 0, 0, 7, 8, 9, 5, 8, 3, 5, 2, 7, 1, 5, 5, 6, 0, 4, 4, 6, 7, 8, 5, 0, 0, 5, 4, 0, 0, 8, 5, 4, 7, 4, 3, 9, 0, 4, 5, 8, 3, 4, 8, 9, 2, 4, 4, 0, 9, 6, 0, 7, 5, 4, 0, 6, 2, 9, 4, 0, 7, 8, 2, 4, 3, 5, 3, 4, 5, 3, 1, 8, 6, 0, 8, 9, 6, 2, 6, 9, 2, 7
OFFSET
0,1
LINKS
FORMULA
Equals lim inf_{n->oo} Product_{k=0..floor(log_6(n))} floor(n/6^k)*6^k/n.
Equals lim inf_{n->oo} A132030(n)/n^(1+floor(log_6(n)))*6^(1/2*(1+floor(log_6(n)))*floor(log_6(n))).
Equals lim inf_{n->oo} A132030(n)/n^(1+floor(log_6(n)))*6^A000217(floor(log_6(n))).
Equals (1/2)*exp(-Sum_{n>0} 6^(-n)*Sum{k|n} 1/(k*2^k)).
Equals lim inf_{n->oo} A132030(n)/A132030(n+1).
Equals (1/2)*(1/12; 1/6)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 20 2015
Equals Product_{n>=1} (1 - 1/A167747(n)). - Amiram Eldar, May 09 2023
EXAMPLE
0.45071262522603913...
MATHEMATICA
digits = 103; NProduct[1-1/(2*6^k), {k, 0, Infinity}, NProductFactors -> 200, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
(1/2)*N[QPochhammer[1/12, 1/6], 200] (* G. C. Greubel, Dec 20 2015 *)
PROG
(PARI) prodinf(x=0, 1-1/(2*6^x)) \\ Altug Alkan, Dec 20 2015
KEYWORD
nonn,cons
AUTHOR
Hieronymus Fischer, Aug 14 2007
STATUS
approved