A132026 Decimal expansion of Product_{k>=0} (1 - 1/(2*10^k)).

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

Offset: 0

Author

Hieronymus Fischer, Jul 28 2007

Keywords

• nonn
• cons

Examples

			0.472362443816572236551413383332...
		

Crossrefs

Cf. A000217, A067080, A093136, A098844, A132019.

Programs

Mathematica

digits = 103; Product[1-1/(2*10^k), {k, 0, Infinity}] // N[#, digits+1]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
RealDigits[QPochhammer[1/2, 1/10], 10, 100][[1]] (* Jan Mangaldan, Jan 04 2017 *)

PARI

prodinf(k=0, 1 - 1/(2*10^k)) \\ Amiram Eldar, May 09 2023

Formula

Equals lim inf_{n->oo} Product_{k=0..floor(log_10(n))} floor(n/10^k)*10^k/n.

Equals lim inf_{n->oo} A067080(n)/n^(1+floor(log_10(n)))*10^(1/2*(1+floor(log_10(n)))*floor(log_10(n))).

Equals lim inf_{n->oo} A067080(n)/n^(1+floor(log_10(n)))*10^A000217(floor(log_10(n))).

Equals lim inf_{n->oo} A067080(n)/A067080(n+1).

Equals 1/2*exp(-Sum_{n>0} 10^(-n)*Sum_{k|n} 1/(k*2^k)).

Equals Product_{n>=1} (1 - 1/A093136(n)). - Amiram Eldar, May 09 2023