A132265 Decimal expansion of Product_{k>=0} (1 - 1/(2*11^k)).

4, 7, 5, 1, 0, 4, 1, 2, 7, 5, 0, 7, 6, 0, 3, 1, 0, 5, 3, 9, 7, 5, 6, 4, 4, 4, 7, 2, 9, 4, 6, 9, 7, 6, 9, 4, 3, 3, 6, 9, 7, 1, 9, 2, 1, 1, 7, 0, 8, 5, 1, 1, 6, 3, 8, 0, 0, 7, 7, 3, 6, 6, 5, 4, 1, 3, 0, 4, 7, 5, 4, 4, 5, 7, 2, 4, 8, 7, 7, 3, 7, 2, 3, 0, 8, 4, 3, 7, 6, 9, 3, 7, 4, 4, 1, 6, 8, 2, 4, 9, 8, 2, 2, 7, 3

Offset: 0

Author

Hieronymus Fischer, Aug 20 2007

Keywords

• nonn
• cons

Examples

			0.47510412750760310539756444...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1500
• Eric Weisstein's World of Mathematics, q-Pochhammer Symbol

Crossrefs

Cf. A000217, A132019-A132026, A132034-A132038, A132263, A132266-A132268, A132323-A132326.

Programs

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 *)

PARI

prodinf(x=0, 1 - 1/(2*11^x)) \\ Altug Alkan, Dec 01 2015

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.

lim inf A132263(n)*11^A000217(floor(log_11(n)))/n^(1+floor(log_11(n))) for n-->oo.

(1/2)*exp(-Sum_{n>0} 11^(-n)*Sum_{k|n} 1/(k*2^k)).

lim inf A132263(n)/A132263(n+1) = 0.47510412750760310539756444... for n-->oo.

Equals (1/2; 1/11){infinity}, where (a;q){infinity} is the q-Pochhammer symbol. - G. C. Greubel, Nov 30 2015