A132023 Decimal expansion of Product_{k>=0} 1-1/(2*7^k).

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

Offset

0,1

Links

Table of n, a(n) for n=0..102.

Formula

Equals lim inf_{n->oo} Product_{k=0..floor(log_7(n))} floor(n/7^k)*7^k/n.

Equals lim inf_{n->oo} A132031(n)/n^(1+floor(log_7(n)))*7^(1/2*(1+floor(log_7(n)))*floor(log_7(n))).

Equals lim inf_{n->oo} A132031(n)/n^(1+floor(log_7(n)))*7^A000217(floor(log_7(n))).

Equals 1/2*exp(-Sum_{n>0} 7^(-n)*Sum_{k|n} 1/(k*2^k)).

Equals lim inf_{n->oo} A132031(n)/A132031(n+1).

Equals Product_{n>=1} (1 - 1/A109808(n)). - Amiram Eldar, May 08 2023

Example

0.4587667266997689850200...

Mathematica

digits = 103; NProduct[1-1/(2*7^k), {k, 0, Infinity}, NProductFactors -> 200, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
RealDigits[QPochhammer[1/2, 1/7], 10, 120][[1]] (* Amiram Eldar, May 08 2023 *)

Crossrefs

Cf. A048651, A098844, A067080, A132019, A132026, A132031, A132035, A000217, A109808.

Sequence in context: A296495 A020804 A021222 * A107758 A104883 A154885

Adjacent sequences: A132020 A132021 A132022 * A132024 A132025 A132026

Keyword

nonn,cons

Author

Hieronymus Fischer, Aug 14 2007

Status

approved