OFFSET
-1,3
COMMENTS
Suggested by Henry Baker in a message to the math-fun mailing list, Mar 16 2018.
FORMULA
Set a(-1) = 0; a(0) = 1; a(n+1) = c(n) * a(n) - a(n-1), where t(0) = 2*Pi, c(n) = ceiling (t(n)), and t(n+1) = 1/(c(n) - t(n)).
EXAMPLE
The best integer over-estimate of 2*Pi is 7. Between 2*Pi and 7 the rational with the smallest denominator is 13/2. Between 2*Pi and 13/2, the rational with the smallest denominator is 19/3. So a(1) = 7, a(2) = 13, a(3) = 19.
CROSSREFS
Cf. A046995, a similar sequence of numerators of rationals converging to 2*Pi, the traditional continued fraction convergents.
KEYWORD
frac,nonn
AUTHOR
Allan C. Wechsler, Mar 18 2018
EXTENSIONS
Offset corrected by Altug Alkan, Mar 19 2018
More terms from Altug Alkan and N. J. A. Sloane (independently), Mar 19 2018
a(-1) = 0 prepended by Altug Alkan, Mar 26 2018
STATUS
approved