%I #32 Mar 26 2018 11:44:51
%S -1,0,1,2,3,7,60,113,16664,33215,49766,364913,1044973,1725033,
%T 14480324,27235615,39990906,52746197,65501488,405764219,2369083826,
%U 9070571085,15772058344,22473545603,29175032862,35876520121,42578007380,49279494639,55980981898,62682469157,69383956416,76085443675,82786930934,89488418193
%N Denominators of successive rational approximations converging to 2*Pi from above for n >= 1, with a(-1) = -1 and a(0) = 0.
%C Suggested by Henry Baker in a message to the math-fun mailing list, Mar 16 2018.
%F Set a(-1) = -1; a(0) = 0; 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)).
%e 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) = 1, a(2) = 2, a(3) = 3. [Corrected by _Altug Alkan_, Mar 19 2018]
%Y Cf. A298737.
%K frac,sign
%O -1,4
%A _Allan C. Wechsler_, Mar 18 2018
%E More terms from _N. J. A. Sloane_, Mar 19 2018
%E a(-1) = -1 and a(0) = 0 prepended by _Altug Alkan_, Mar 26 2018