OFFSET
1,1
COMMENTS
Through any A085368(n) number of terms in the cutting sequence, A007677(n-1) of those terms are zeros and A007676(n) are ones. Check: A085368(5) = 26, the sequence being 3, 4, 11, 15, 26, ... (sum of numerators and denominators of convergents to 1/e). Then through n=26, A085369(n) is 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0, with 7 zeros and 19 ones, (7/19 being the 5th convergent to 1/e): 7/19 = [2, 1, 2, 1, 1]. Numerator and denominator sum = 26, with 7 zeros and 19 ones, with the zeros occupying positions n = 3, 7, 11, 14, 18, 22 and 26 (also being the first 7 terms of A000572). Positions of the cutting sequence occupied by ones (1, 2, 4, 5, 6, ...) are consecutive terms of the lower Beatty sequence A006594, being generated by floor(n*(1 + 1/e)).
REFERENCES
Manfred R. Schroeder, "Fractals, Chaos, Power Laws", Freeman, 1996, p. 56.
FORMULA
Given the line y = (1/e)x starting from (0, 0) and passing through an array of squares, a "1" denotes an intersection with a vertical line, while an "0" denotes an intersection with a horizontal line.
EXAMPLE
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jun 26 2003
STATUS
approved