A160272 Angle between the two hands of a 12 hour analog clock n*12 minutes after noon/midnight, measured in units of minutes.

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

Offset

0,2

Comments

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.

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 hour-hand 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 minute-marking and the hour hand points at the 1st minute-marking (N=11).
At 00:36, the minute hand points at the 36th minute-marking and the hour hand points at the 3rd minute-marking, 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 360-m; 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 A366093 A178736

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