A181874 -id:A181874 - cp's OEIS frontend

A178181 Minute with hour hand overlap problem on analog clock.

0, 5, 10, 16, 21, 27, 32, 38, 43, 49, 54

Offset: 0

Wolfdieter Lang, Dec 20 2010

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).

			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.

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.

Cf. A183032 (seconds). A181874.

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

A183032 Seconds (rounded down) at which the minute hand overlaps with hour hand on the analog clock.

Original entry on oeis.org

0, 27, 54, 21, 49, 16, 43, 10, 38, 5, 32

Offset: 0

Wolfdieter Lang, Dec 20 2010

At which a.m. times h:m:s (with fractions of seconds) does the minute hand overlap with the hour hand on an analog clock? This is problem 43 of the quoted Loyd/Gardner book where also the solution is given (pp. 41-2, solution pp. 180-1 in the German version).
a(n) gives the full second 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 minute is A178181(n), and the fraction of the second is A183033(n)/11.
For the same problem on an analog quartz clock (discrete seconds) the best approximation with rounded seconds is given in A181874.

			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.

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.

Cf. A178181 (minutes), A181874.

Table[ Floor@ Mod[300/11 n, 60], {n, 0, 10}]

a(n) = floor(300*n/11) (mod 60), n=0..10.

cp's OEIS Frontend

A178181 Minute with hour hand overlap problem on analog clock.

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