login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A076393 Decimal expansion of Vardi constant arising in the Sylvester sequence. 13
1, 2, 6, 4, 0, 8, 4, 7, 3, 5, 3, 0, 5, 3, 0, 1, 1, 1, 3, 0, 7, 9, 5, 9, 9, 5, 8, 4, 1, 6, 4, 6, 6, 9, 4, 9, 1, 1, 1, 4, 5, 6, 0, 1, 7, 9, 2, 0, 9, 0, 6, 5, 5, 3, 3, 1, 5, 3, 4, 5, 6, 4, 1, 9, 9, 0, 7, 7, 5, 9, 0, 1, 6, 3, 6, 2, 9, 5, 1, 6, 0, 1, 4, 2, 2, 6, 3, 9, 0, 9, 2, 6, 8, 3, 9, 8, 5, 1, 5, 0, 4, 8, 0, 3, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Vardi showed A000058(n) = floor(c^(2^(n+1))+1/2) where c=1.26408473...

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 443-448.

Ilan Vardi, Computational Recreations in Mathematica, Addison-Wesley, pp. 82-89, 1991.

LINKS

Table of n, a(n) for n=1..105.

Matthew Brendan Crawford, On the Number of Representations of One as the Sum of Unit Fractions, Master's Thesis, Virginia Polytechnic Institute and State University (2019).

B. Nill, Volume and lattice points of reflexive simplices, arXiv:math/0412480 [math.AG], 2004-2007.

Eric Weisstein's World of Mathematics, Sylvester's Sequence

FORMULA

Equals lim_{n->infinity} A000058(n)^(1/2^(n+1)). - Robert FERREOL, Feb 15 2019

EXAMPLE

1.26408473530530111307959958416466949111456...

MATHEMATICA

digits = 105; For[c = 2; olds = -1; s = 0; j = 1, RealDigits[olds, 10, digits+5] != RealDigits[s, 10, digits+5], j++; c = c^2-c+1, olds = s; s = s + 2^(-j-1)*Log[1+(2*c-1)^-2] // N[#, digits+5]&]; chi = Sqrt[6]/2*Exp[s]; RealDigits[chi, 10, digits] // First (* Jean-Fran├žois Alcover, Jun 05 2014 *)

CROSSREFS

Cf. A000058.

Sequence in context: A077750 A332253 A247493 * A054674 A186503 A213654

Adjacent sequences:  A076390 A076391 A076392 * A076394 A076395 A076396

KEYWORD

cons,easy,nonn

AUTHOR

Benoit Cloitre, Nov 06 2002

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 03:51 EDT 2021. Contains 343199 sequences. (Running on oeis4.)