A160278 Angle in degrees between the two hands of a 12-hour analog clock at 12*n minutes after noon/midnight.

0, 66, 132, 162, 96, 30, 36, 102, 168, 126, 60, 6, 72, 138, 156, 90, 24, 42, 108, 174, 120, 54, 12, 78, 144, 150, 84, 18, 48, 114, 180, 114, 48, 18, 84, 150, 144, 78, 12, 54, 120, 174, 108, 42, 24, 90, 156, 138, 72, 6, 60, 126, 168, 102, 36, 30, 96, 162, 132, 66

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 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.

Links

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

Formula

a(n) = a(n-60), n >= 60 (24-hr period).

a(30-n) = a(30+n), 0 <= n <= 30 (reversal at 06:00).

Example

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).
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).

Maple

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

Crossrefs

Cf. A160272.

Sequence in context: A044570 A118163 A160848 * A206030 A174929 A072430

Adjacent sequences: A160275 A160276 A160277 * A160279 A160280 A160281

Keyword

nonn,easy

Author

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

Extensions

Edited, 112 replaced with 102, by R. J. Mathar, May 12 2009

Status

approved