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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124118 Decimal expansion of Sum_{i>=0} A004018(i)/2^i. 2
4, 5, 3, 2, 3, 7, 2, 0, 1, 4, 2, 5, 8, 9, 7, 4, 1, 0, 0, 8, 2, 7, 9, 5, 7, 1, 7, 8, 6, 6, 0, 4, 7, 1, 1, 9, 3, 5, 5, 7, 2, 2, 9, 3, 2, 6, 0, 8, 7, 8, 8, 7, 4, 1, 0, 0, 6, 7, 7, 3, 4, 8, 9, 4, 5, 6, 8, 5, 7, 7, 4, 7, 0, 0, 8, 3, 4, 2, 8, 5, 5, 1, 9, 5, 9, 0, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, 6 ed., 2008, section 17.10, p. 340.
LINKS
D. H. Bailey, J. M. Borwein, R. E. Crandall and C. Pomerance, On the binary expansions of algebraic numbers, Journal de Théorie des Nombres de Bordeaux 16 (2004), 487-518. LBNL-53854.
Simon Plouffe, Constants derived from sums of A004018 [broken link?].
FORMULA
Sum_{i>=0} A004018(i)/2^i.
Bailey et al. point out the approximation Pi*(1+2*exp(-Pi^2/log(2))^2)/log(2), correct up to 23 decimal places. - Jean-François Alcover, Jun 27 2015
Equals 1 + 4 * Sum_{k>=0} (-1)^k/(2^(2*k+1) - 1). - Amiram Eldar, Jun 22 2020
EXAMPLE
4.532372014258974100827957178...
MATHEMATICA
Clear[s]; s[n_] := s[n] = RealDigits[ Sum[ SquaresR[2, k]/2^k, {k, 0, n}], 10, 29] // First; s[n=100]; While[s[n] != s[n-100], n = n+100]; s[n] (* Jean-François Alcover, Feb 13 2013 *)
RealDigits[1 + 4*Sum[(-1)^n/(2^(2*n + 1) - 1), {n, 0, 200}], 10, 100][[1]] (* Amiram Eldar, Jun 22 2020 *)
CROSSREFS
Cf. A004018.
Sequence in context: A094850 A163973 A369500 * A016716 A004485 A057113
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Nov 25 2006
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 June 20 12:38 EDT 2024. Contains 373527 sequences. (Running on oeis4.)