cp's OEIS Frontend

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.

%I A120500 #17 Nov 19 2021 15:14:49
%S A120500 0,10527,21055,31622,42149,52716,63244,73811,84338,94905,105433,120000
%N 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.
%C A120500 A subsequence of A121577. - _Lekraj Beedassy_, Aug 09 2006
%D A120500 M. Gardner, Science Fiction Puzzle Tales, Problem 28 pp. 90;141 Clarkson N. Potter NY 1981.
%D A120500 M. Gardner, Mathematical Puzzles of Sam Loyd, Problem 43 pp. 40;137 Dover NY 1959.
%D A120500 A. Jouette, Le Secret Des Nombres, Problem 52 pp. 176;269 Albin Michel Paris 1996.
%H A120500 T. Eveilleau, <a href="http://therese.eveilleau.pagesperso-orange.fr/pages/paradoxe/textes/horloge.htm">Les aiguilles de l'horloge</a> (in French).
%F A120500 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.
%e A120500 52716, for instance, in the sequence is meant to be read 5:27:16 or 5hr27mn16s.
%e A120500 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.
%t A120500 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 *)
%Y A120500 Cf. A348758, A348759.
%K A120500 fini,full,nonn
%O A120500 0,2
%A A120500 _Lekraj Beedassy_, Aug 06 2006