|
|
A073115
|
|
Decimal expansion of sum(k>=0, 1/2^floor(k*phi) ) where phi = (1+sqrt(5))/2.
|
|
6
|
|
|
1, 7, 0, 9, 8, 0, 3, 4, 4, 2, 8, 6, 1, 2, 9, 1, 3, 1, 4, 6, 4, 1, 7, 8, 7, 3, 9, 9, 4, 4, 4, 5, 7, 5, 5, 9, 7, 0, 1, 2, 5, 0, 2, 2, 0, 5, 7, 6, 7, 8, 6, 0, 5, 1, 6, 9, 5, 7, 0, 0, 2, 6, 4, 4, 6, 5, 1, 2, 8, 7, 1, 2, 8, 1, 4, 8, 4, 6, 5, 9, 6, 2, 4, 7, 8, 3, 1, 6, 1, 3, 2, 4, 5, 9, 9, 9, 3, 8, 8, 3, 9, 2, 6, 5, 3
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Number whose digits are obtained from the substitution system (1->(1,0),0->(1)).
The n-th term of the continued fraction is 2^Fibonacci(n-2) ) (cf. A000301).
This number is known to be transcendental.
|
|
REFERENCES
|
S. Wolfram, "A new kind of science", p. 913
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
1.70980344286129131464178739944457559701250220576786...
|
|
MATHEMATICA
|
Take[ RealDigits[ Sum[N[1/2^Floor[k*GoldenRatio], 120], {k, 0, 300}]][[1]], 105] (* Jean-François Alcover, Jul 28 2011 *)
|
|
PROG
|
(PARI) phi=(1+sqrt(5))/2; suminf(n=1, (phi*n\1)/2^n) - 1 /* Michael Somos, May 22 2021 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|