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A181874 Minute hand closest to hour hand on analog quartz clock. Best approximation for seconds.

%I A181874 #6 Jan 20 2014 22:13:30
%S A181874 0,27,55,22,49,16,44,11,38,5,33
%N A181874 Minute hand closest to hour hand on analog quartz clock. Best approximation for seconds.
%C A181874 At which a.m. times h:m:s is the minute hand closest to the hour hand on an analog quartz clock (discrete seconds)? For an analog clock with continuous seconds this is the overlap problem nr. 43 of the quoted Loyd/Gardner book where also the solution is given (pp. 41-2, solution pp. 180-1 in the German version). See A183032.
%D A181874 Sam Loyd, Mathematische Raetsel und Spiele, ausgewaehlt und herausgegeben von Martin Gardner, Dumont, Koeln, 1978, 3. Auflage 1997.
%D A181874 Sam Loyd, Mathematical puzzles, selected and edited by Martin Gardner, Dover, 1959.
%F A181874 a(n) gives the second for the (a.m.) hour h=n = 0,1,2,...,10, when the minute hand is closest to the hour hand on an analog quartz clock (discrete seconds), provided the minute is A178181(n).
%F A181874 a(n)= round((300/11)*n) (mod 60), n=0..10. See the solution in the Loyd book with (27+3/11)s = 300/11 s.
%e A181874 The eleven times are:
%e A181874 00:00:00, 01:05:27, 02:10:55, 03:16:22,
%e A181874 04:21:49, 05:27:16, 06:32:44, 07:38:11,
%e A181874 08:43:38, 09:49:05, 10:54:33.
%e A181874 The next time would be 12:00:00
%Y A181874 Cf.: A178181, A183032, A183033.
%K A181874 nonn,fini,easy
%O A181874 0,2
%A A181874 _Wolfdieter Lang_, Jan 21 2011