A183033 -id:A183033 - 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.

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

Original entry on oeis.org

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

Offset: 0

Wolfdieter Lang, Jan 21 2011

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.

			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

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, A183032, A183033.

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.

A242063 Analog clock times where the minute hand is on the hour hand (in hhmm format).

Original entry on oeis.org

0, 105, 211, 316, 422, 527, 633, 738, 844, 949, 1055

Offset: 1

Jon Perry, Aug 13 2014

The format is loosely defined - leading zeros of both hours and minutes disappear.
Changing the tolerance in the JavaScript program changes the results - try 0.01 for example, and we are allowed 10:54.
It is debatable whether 00:00 should be 12:00, but I have used 00:00. As the clock is analog, 13:05 is not valid - am and pm is usually left to discretion.

			At 04:22 the minute hand covers the hour hand.

Maths is Fun, Analog Clock
Maths is Fun, Set the time
NAWCC, How do clocks work?
Wikipedia, Clocks
Wikipedia, Watches

Cf. A178181, A183032, A183033.

for (h=0;h<12;h++)
for (m=0;m<60;m++)
if (Math.abs(h/12+m/720-m/60)<0.007) {if (m<10) m="0"+m;document.write(h.toString()+m+", ");}

a(n) = a(n-1) + a(n-2) - a(n-3) for n=4..11. - Colin Barker, Aug 19 2014

a(n) = (-423 - (-1)^n + 422*n)/4 for n=1..11. - Colin Barker, Aug 19 2014

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A178181 Minute with hour hand overlap problem on analog clock.

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

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

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A242063 Analog clock times where the minute hand is on the hour hand (in hhmm format).

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