cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Views

Author

Wolfdieter Lang, Dec 20 2010

Keywords

Comments

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.

Examples

			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.

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.

Crossrefs

Cf. A178181 (minutes), A181874.

Programs

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

Formula

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

A183033 Minute with hour hand overlap problem on analog clock. Fractions of seconds.

Original entry on oeis.org

0, 3, 6, 9, 1, 4, 7, 10, 2, 5, 8
Offset: 0

Views

Author

Wolfdieter Lang, Dec 20 2010

Keywords

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 referenced Loyd/Gardner book, which also gives the solution (pp. 41-42, solution pp. 180-181 in the German version).

Examples

			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.

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.

Programs

  • Mathematica
    Table[ Mod[ Floor[300/11 n], 12], {n, 0, 10}]

Formula

a(n)/11 gives the fraction of the 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 full second is A183032(n). See the eleven times given in EXAMPLE.
a(n) = floor((300*n)/11) (mod 12), n=0..10. (See the Mathematica code given by Robert G. Wilson v, and also the solution in Loyd's book with (27 + 3/11)s = 300/11 s.)

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

Views

Author

Wolfdieter Lang, Jan 21 2011

Keywords

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.

Examples

			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

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.

Crossrefs

Cf.: A178181, A183032, A183033.

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.

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

Views

Author

Jon Perry, Aug 13 2014

Keywords

Comments

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.

Examples

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

Links

Crossrefs

Cf. A178181, A183032, A183033.

Programs

  • JavaScript
    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+", ");}

Formula

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

A291092 1 followed by infinitely many 9's.

Original entry on oeis.org

1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
Offset: 1

Views

Author

N. J. A. Sloane, Aug 19 2017

Keywords

Comments

The digital root of 9^(n-1). - Cino Hilliard, Dec 31 2004
With interpolated zeros (1,0,9,0,9,0,9,0,...) this is the number of hours between times when the hands of a two-handed clock cross. - Halfdan Skjerning, Aug 18 2017

Links

Crossrefs

Cf. A178181, A010734, A180599, A100403, A100401.

Programs

  • Mathematica
    PadRight[{1},100,9] (* Paolo Xausa, Oct 16 2023 *)

Formula

G.f.: x*(1 + 8*x)/(1 - x). - Chai Wah Wu, Aug 19 2017
E.g.f.: 9*(exp(x) - 1) - 8*x. - Stefano Spezia, Oct 16 2023
Showing 1-5 of 5 results.

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