

A160272


Angle between the two hands of a 12 hour analog clock n*12 minutes after noon/midnight, measured in units of minutes.


2



0, 11, 22, 27, 16, 5, 6, 17, 28, 21, 10, 1, 12, 23, 26, 15, 4, 7, 18, 29, 20, 9, 2, 13, 24, 25, 14, 3, 8, 19, 30, 19, 8, 3, 14, 25, 24, 13, 2, 9, 20, 29, 18, 7, 4, 15, 26, 23, 12, 1, 10, 21, 28, 17, 6, 5, 16, 27, 22, 11
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OFFSET

0,2


COMMENTS

The hourhand movement is "quantized": the hourhand has 60 "states" between minutemark 0 and minutemark 59; the minute hand is thus constrained to 12minute steps.
The angle is defined as the smaller of the two angles, the one in the range 0 to 180 degrees. The sequence reverses at 06:00 (angle N=30 minutes), and recycles from N=0 at 12:00.
Other times can have any gap between 0 and 30 minutes, but they will not have the hourhand precisely registered (e.g., 04:54:32.73 has a 30 minute gap, but the hour hand has moved off the 54th mark).


LINKS

Table of n, a(n) for n=0..59.


FORMULA

a(n) = A160278(n)/6.


EXAMPLE

00:00 has no gap between hands viewed normally (N=0); at 00:12, the minute hand points at the 12th minutemarking and the hour hand points at the 1st minutemarking (N=11).
At 00:36, the minute hand points at the 36th minutemarking and the hour hand points at the 3rd minutemarking, but N<>33, because the minimum gap is found clockwise: 24 +3 (N=27).


MAPLE

A160278 := proc(n) m := (n*66 ) mod 360 ; if m < 180 then m; else 360m; fi; end: A160272 := proc(n) A160278(n)/6 ; end: seq(A160272(n), n=0..60) ; # R. J. Mathar, May 12 2009


CROSSREFS

Cf. A160278.
Sequence in context: A066500 A234314 A258738 * A164006 A178736 A054728
Adjacent sequences: A160269 A160270 A160271 * A160273 A160274 A160275


KEYWORD

nonn


AUTHOR

William A. Hoffman III (whoff(AT)robill.com), May 07 2009


EXTENSIONS

Edited by R. J. Mathar, May 12 2009


STATUS

approved



