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%I #6 Feb 13 2019 03:53:55
%S 0,66,132,162,96,30,36,102,168,126,60,6,72,138,156,90,24,42,108,174,
%T 120,54,12,78,144,150,84,18,48,114,180,114,48,18,84,150,144,78,12,54,
%U 120,174,108,42,24,90,156,138,72,6,60,126,168,102,36,30,96,162,132,66
%N Angle in degrees between the two hands of a 12-hour analog clock at 12*n minutes after noon/midnight.
%C The hour-hand movement is "quantized": the hour-hand has 60 "states" between minute-mark 0 and minute-mark 59; the minute hand is thus constrained to 12-minute steps.
%C The angle A is defined as the smaller of the two angles, the one reduced to the range from 0 to 180 degrees. The sequence reverses at 06:00 (A=180), and recycles from A=0 at 12:00.
%F a(n) = a(n-60), n >= 60 (24-hr period).
%F a(30-n) = a(30+n), 0 <= n <= 30 (reversal at 06:00).
%e 00:00 has no angle between hands viewed normally (A=0); at 00:12, the minute hand points at the 12th minute-marking and the hour hand points at the 1st minute-marking (A=66); at 00:36, the minute hand points at the 36th minute-marking and the hour hand points at the 3rd minute-marking, but A <> 198, because the minimum gap is found clockwise from the minute hand: 144 + 18 (A=162).
%e Other times can have any gap between 0 and 180 degrees, but they will not have the hour-hand precisely registered (e.g., 04:54:32.73 has a 180 degree gap, but the hour hand has moved off the 54th mark).
%p A160278 := proc(n) m := (n*66) mod 360; if m < 180 then m; else 360-m; fi; end: seq(A160278(n),n=0..60) ; # _R. J. Mathar_, May 12 2009
%Y Cf. A160272.
%K nonn,easy
%O 0,2
%A William A. Hoffman III (whoff(AT)robill.com), May 07 2009
%E Edited, 112 replaced with 102, by _R. J. Mathar_, May 12 2009
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