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A183032 Seconds (rounded down) at which the minute hand overlaps with hour hand on the analog clock.

%I A183032 #25 Sep 23 2021 05:12:18
%S A183032 0,27,54,21,49,16,43,10,38,5,32
%N A183032 Seconds (rounded down) at which the minute hand overlaps with hour hand on the analog clock.
%C A183032 At which a.m. times h:m:s (with fractions of seconds) does the minute hand overlap with the hour hand on an analog clock? This is problem 43 of the quoted Loyd/Gardner book where also the solution is given (pp. 41-2, solution pp. 180-1 in the German version).
%C A183032 a(n) gives the full second for the (a.m.) hour h=n = 0,1,2,...,10, when the minute hand overlaps the hour hand on an analog clock, provided the minute is A178181(n), and the fraction of the second is A183033(n)/11.
%C A183032 For the same problem on an analog quartz clock (discrete seconds) the best approximation with rounded seconds is given in A181874.
%D A183032 Sam Loyd, Mathematische Raetsel und Spiele, ausgewaehlt und herausgegeben von Martin Gardner, Dumont, Koeln, 1978, 3. Auflage 1997.
%D A183032 Sam Loyd, Mathematical puzzles, selected and edited by Martin Gardner, Dover, 1959.
%F A183032 a(n) = floor(300*n/11) (mod 60), n=0..10.
%e A183032 The eleven overlap times are:
%e A183032 00:00:00 plus 0/11 s, 01:05:27 plus 3/11 s;
%e A183032 02:10:54 plus 6/11 s, 03:16:21 plus 9/11 s,
%e A183032 04:21:49 plus 1/11 s, 05:27:16 plus 4/11 s,
%e A183032 06:32:43 plus 7/11 s, 07:38:10 plus 10/11 s,
%e A183032 08:43:38 plus 2/11 s, 09:49:05 plus 5/11 s,
%e A183032 10:54:32 plus 8/11 s.
%e A183032 The next time would be 12:00:00.
%t A183032 Table[ Floor@ Mod[300/11 n, 60], {n, 0, 10}]
%Y A183032 Cf. A178181 (minutes), A181874.
%K A183032 nonn,fini,full,easy
%O A183032 0,2
%A A183032 _Wolfdieter Lang_, Dec 20 2010