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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. 5
0, 10527, 21055, 31622, 42149, 52716, 63244, 73811, 84338, 94905, 105433, 120000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A subsequence of A121577. - Lekraj Beedassy, Aug 09 2006
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).
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.
EXAMPLE
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.
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 *)
CROSSREFS
Sequence in context: A235119 A236036 A216489 * A157487 A203666 A346892
KEYWORD
fini,full,nonn
AUTHOR
Lekraj Beedassy, Aug 06 2006
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)