The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A183033 Minute with hour hand overlap problem on analog clock. Fractions of seconds. 4
 0, 3, 6, 9, 1, 4, 7, 10, 2, 5, 8 (list; graph; refs; listen; history; text; internal format)
 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 referenced Loyd/Gardner book, which also gives the solution (pp. 41-42, solution pp. 180-181 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, 1959. LINKS 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.) 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. MATHEMATICA Table[ Mod[ Floor[300/11 n], 12], {n, 0, 10}] CROSSREFS Sequence in context: A247398 A094560 A179615 * A199735 A198143 A131579 Adjacent sequences:  A183030 A183031 A183032 * A183034 A183035 A183036 KEYWORD nonn,fini,full,easy AUTHOR Wolfdieter Lang, Dec 20 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)