VOOZH about

URL: https://oeis.org/A178181

⇱ A178181 - OEIS

login
A178181
Minute with hour hand overlap problem on analog clock.
5
0, 5, 10, 16, 21, 27, 32, 38, 43, 49, 54
OFFSET
0,2
COMMENTS
At which a.m. times h:m:s (with fractions of seconds) does the minute hand overlap the hour hand on an analog clock? This is Problem 43 of the quoted Loyd/Gardner book (pp. 41-42, solution pp. 180-1 in the German version).
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 Publications, NY, 1959.
FORMULA
a(n) gives the full minute for the (a.m.) hour h=n = 0,1,2,...,10, when the minute hand overlaps the hour hand on an analog clock, provided the second is A183032(n) + A183033(n)/11.
a(n)= floor((720/11)*n) (mod 60), n=0..10. See the solution in Loyd's book with (65+5/11)m = 720/11 m.
Note that 60/11 m = (5+5/11)m.
See the eleven times given in EXAMPLE.
a(n) = a(n-1)+a(n-2)-a(n-3) for n=4..10. - Colin Barker, Aug 19 2014
a(n) = (-3-(-1)^n+22*n)/4 for n=1..10. - Colin Barker, Aug 19 2014
EXAMPLE
The eleven overlap times are:
00:00:00 plus 0/11 s, 01:05:27 plus 3/11 s;
02:10:54 plus 6/11 s, 03:16:21 plus 9/11 s,
04:21:49 plus 1/11 s, 05:27:16 plus 4/11 s,
06:32:43 plus 7/11 s, 07:38:10 plus 10/11 s,
08:43:38 plus 2/11 s, 09:49:05 plus 5/11 s,
10:54:32 plus 8/11 s.
The next time would be 12:00:00.
CROSSREFS
Cf. A183032 (seconds). A181874.
Sequence in context: A313893 A313894 A276853 * A277645 A075003 A313895
KEYWORD
nonn,easy,fini,full
AUTHOR
Wolfdieter Lang, Dec 20 2010
STATUS
approved