A181874 Minute hand closest to hour hand on analog quartz clock. Best approximation for seconds.

0, 27, 55, 22, 49, 16, 44, 11, 38, 5, 33

Offset

0,2

Comments

At which a.m. times h:m:s is the minute hand closest to the hour hand on an analog quartz clock (discrete seconds)? For an analog clock with continuous seconds this is the overlap problem nr. 43 of the quoted Loyd/Gardner book where also the solution is given (pp. 41-2, solution pp. 180-1 in the German version). See A183032.

References

Sam Loyd, Mathematische Raetsel und Spiele, ausgewaehlt und herausgegeben von Martin Gardner, Dumont, Koeln, 1978, 3. Auflage 1997.

Sam Loyd, Mathematical puzzles, selected and edited by Martin Gardner, Dover, 1959.

Links

Table of n, a(n) for n=0..10.

Formula

a(n) gives the second for the (a.m.) hour h=n = 0,1,2,...,10, when the minute hand is closest to the hour hand on an analog quartz clock (discrete seconds), provided the minute is A178181(n).

a(n)= round((300/11)*n) (mod 60), n=0..10. See the solution in the Loyd book with (27+3/11)s = 300/11 s.

Example

The eleven times are:
00:00:00, 01:05:27, 02:10:55, 03:16:22,
04:21:49, 05:27:16, 06:32:44, 07:38:11,
08:43:38, 09:49:05, 10:54:33.
The next time would be 12:00:00

Crossrefs

Cf.: A178181, A183032, A183033.

Sequence in context: A175806 A232922 A306761 * A042444 A042442 A042440

Adjacent sequences: A181871 A181872 A181873 * A181875 A181876 A181877

Keyword

nonn,fini,easy

Author

Wolfdieter Lang, Jan 21 2011

Status

approved