A132024 Decimal expansion of Product_{k>=0} (1-1/(2*8^k)).

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

Offset: 0

Author

Hieronymus Fischer, Aug 14 2007

Keywords

• nonn
• cons

Examples

			0.46456888368647639098...
		

Crossrefs

Cf. A048651, A098844, A067080, A132019, A132026, A132032, A132036, A000217, A013730.

Programs

Mathematica

RealDigits[QPochhammer[1/2,1/8],10,120][[1]] (* Harvey P. Dale, May 23 2011 *)

PARI

prodinf(k=0, 1 - 1/(2*8^k)) \\ Amiram Eldar, May 09 2023

Formula

Equals lim inf_{n->oo} Product_{k=0..floor(log_8(n))} floor(n/8^k)*8^k/n.

Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^(1/2*(1+floor(log_8(n)))*floor(log_8(n))).

Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^A000217(floor(log_8(n))).

Equals (1/2)*exp(-Sum_{n>0} 8^(-n)*Sum_{k|n} 1/(k*2^k)).

Equals lim inf_{n->oo} A132032(n)/A132032(n+1).

Equals Product_{n>=0} (1 - 1/A013730(n)). - Amiram Eldar, May 09 2023

Extensions

Name corrected by Amiram Eldar, May 09 2023