A120500 Times in hours,minutes and seconds (to the nearest second) at which the smoothly crossing minute and hour hands of an analog clock coincide, over a period of one complete 12-hour sweep of the hour hand.

0, 10527, 21055, 31622, 42149, 52716, 63244, 73811, 84338, 94905, 105433, 120000

Offset: 0

Author

Lekraj Beedassy, Aug 06 2006

Keywords

• fini
• full
• nonn

Comments

A subsequence of A121577. - Lekraj Beedassy, Aug 09 2006

Examples

			52716, for instance, in the sequence is meant to be read 5:27:16 or 5hr27mn16s.
We have a(3)=round(43200*3/11) to base 60(double-spaced), i.e., 11782=3*60^2 +16*60 + 22*1 to base 60, which is 31622.
		

References

• M. Gardner, Science Fiction Puzzle Tales, Problem 28 pp. 90;141 Clarkson N. Potter NY 1981.
• M. Gardner, Mathematical Puzzles of Sam Loyd, Problem 43 pp. 40;137 Dover NY 1959.
• A. Jouette, Le Secret Des Nombres, Problem 52 pp. 176;269 Albin Michel Paris 1996.

Links

• T. Eveilleau, Les aiguilles de l'horloge (in French).

Crossrefs

Cf. A348758, A348759.

Programs

Mathematica

fix[{a_,b_,c_}]:=FromDigits[Flatten[{a,PadLeft[IntegerDigits[b], 2], PadLeft[ IntegerDigits[c],2]}]]; Join[{0},fix/@Table[ IntegerDigits[ Round[(43200n)/11],60],{n,11}]] (* Harvey P. Dale, Oct 05 2017 *)

Formula

a(n)=round(43200*n/11) expressed in double-spaced sexagesimal scale. In other words, the hour and minute hands line up at 11 successive positions after every (12/11)hr, i.e., 1hr5min27s and 3/11s from noon or midnight.