login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132022 Decimal expansion of Product_{k>=0} (1 - 1/(2*6^k)). 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2000

FORMULA

lim inf product{0<=k<=floor(log_6(n)), floor(n/6^k)*6^k/n} for n-->oo.

lim inf A132030(n)/n^(1+floor(log_6(n)))*6^(1/2*(1+floor(log_6(n)))*floor(log_6(n))) for n-->oo.

lim inf A132030(n)/n^(1+floor(log_6(n)))*6^A000217(floor(log_6(n))) for n-->oo.

(1/2)*exp(-sum{n>0, 6^(-n)*sum{k|n, 1/(k*2^k))}}).

lim inf A132030(n)/A132030(n+1)=0.45071262522603913... for n-->oo.

Equals (1/2)*(1/12; 1/6)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Dec 20 2015

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-Fran├žois 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

CROSSREFS

Cf. A000217, A048651, A098844, A067080, A132019, A132026, A132030, A132034.

Sequence in context: A092487 A322505 A192041 * A319459 A318740 A240160

Adjacent sequences:  A132019 A132020 A132021 * A132023 A132024 A132025

KEYWORD

nonn,cons

AUTHOR

Hieronymus Fischer, Aug 14 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 03:10 EDT 2019. Contains 323412 sequences. (Running on oeis4.)