login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158468 Decimal expansion of hz = limit_{k -> infinity} 1 + k - Sum_{j = -k..k} exp(-2^j). 5
1, 3, 3, 2, 7, 4, 7, 3, 8, 2, 4, 3, 2, 8, 9, 9, 2, 2, 5, 0, 0, 8, 6, 0, 1, 0, 9, 8, 3, 7, 3, 8, 9, 9, 7, 0, 4, 4, 1, 6, 7, 4, 3, 9, 8, 2, 2, 5, 9, 8, 4, 4, 5, 3, 6, 5, 7, 9, 7, 1, 8, 4, 9, 3, 9, 9, 3, 3, 4, 1, 6, 8, 8, 2, 7, 3, 5, 4, 7, 4, 5, 4, 0, 7, 0, 2, 8, 0, 6, 5, 1, 7, 1, 6, 6, 6, 0, 4, 7, 8, 7, 0, 4, 0, 6, 6, 8, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Curiously, this constant is close to gamma/log(2)+1/2 = 1.332746177... - Jean-François Alcover, Mar 24 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

Equals gamma/log(2)+1/2 + Sum_{k>=1} Im(Gamma(1-2*k*Pi*i/log(2)))/(k*Pi). - Toshitaka Suzuki, Feb 10 2017

Also equals limit_{k->oo} 1 + Sum_{j>=1} 1-(1-1/2^j)^(2^k). - Toshitaka Suzuki, Feb 12 2017

EXAMPLE

1.3327473824328992250086010983738997044167439822598445365797...

MAPLE

hz:= limit(1+k -sum(exp(-2^j), j=-k..k), k=infinity):

hzs:= convert(evalf(hz/10, 130), string):

seq(parse(hzs[n+1]), n=1..120);

MATHEMATICA

digits = 105; Clear[f]; f[k_] := f[k] = 1 + k - Sum[Exp[-2^j], {j, -k, k}] // RealDigits[#, 10, digits+1]& // First // Quiet; f[1]; f[n=2]; While[f[n] != f[n-1], n++] ; f[n] // Most (* Jean-François Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A100668 (gamma/log(2)), A158469 (continued fraction), A159835 (Engel expansion), A339168.

Sequence in context: A266153 A086636 A115055 * A238278 A200770 A265965

Adjacent sequences: A158465 A158466 A158467 * A158469 A158470 A158471

KEYWORD

nonn,cons

AUTHOR

Alois P. Heinz, Mar 19 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)