A132021 - OEIS

A132021

Decimal expansion of Product_{k>=0} 1-1/(2*5^k).

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

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OFFSET

0,1

LINKS

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

FORMULA

Equals lim inf_{n->oo} Product_{k=0..floor(log_5(n))} floor(n/5^k)*5^k/n.

Equals lim inf_{n->oo} A132029(n)/n^(1+floor(log_5(n)))*5^(1/2*(1+floor(log_5(n)))*floor(log_5(n))).

Equals lim inf_{n->oo} A132029(n)/n^(1+floor(log_5(n)))*5^A000217(floor(log_5(n))).

Equals (1/2)*exp(-Sum_{n>0} 5^(-n)*Sum_{k|n} 1/(k*2^k)).

Equals lim inf_{n->oo} A132029(n)/A132029(n+1).

Equals Product_{n>=0} (1 - 1/A020729(n)). - Amiram Eldar, May 08 2023

EXAMPLE

0.438796837203638531...

MATHEMATICA

digits = 103; NProduct[1-1/(2*5^k), {k, 0, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+5] // N[#, digits+5]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)

RealDigits[QPochhammer[1/2, 1/5], 10, 120][[1]] (* Amiram Eldar, May 08 2023 *)

CROSSREFS

Cf. A048651, A098844, A067080, A132019, A132026, A132029, A100222, A000217, A020729.

Sequence in context: A110662 A265289 A302258 * A089368 A357130 A116583

Adjacent sequences: A132018 A132019 A132020 * A132022 A132023 A132024

KEYWORD

nonn,cons

AUTHOR

Hieronymus Fischer, Aug 14 2007

STATUS

approved