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A335789 a(n) = time to the nearest second at the n-th instant (n>=0) when the hour and minute hands on a clock face coincide, starting at time 0:00. 1

%I #55 Aug 18 2020 13:10:01

%S 0,3927,7855,11782,15709,19636,23564,27491,31418,35345,39273,43200,

%T 47127,51055,54982,58909,62836,66764,70691,74618,78545,82473,86400,

%U 90327,94255,98182,102109,106036,109964,113891,117818,121745,125673,129600,133527,137455,141382

%N a(n) = time to the nearest second at the n-th instant (n>=0) when the hour and minute hands on a clock face coincide, starting at time 0:00.

%C After 12 hours or 43200 seconds, the hands overlap at 12:00 and the cycle repeats.

%H Mathlete's Corner, <a href="https://sites.google.com/site/funproblemsolving/topics-1/how-many-times-during-the-day-do-the-hands-of-a-clock-overlap">How many times during the day do the hands of a clock overlap?</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

%F a(n) = round(n*43200/11).

%e For n=1, 3927 would correspond to slightly after 01:05.

%o (SageMath)

%o L=[]

%o n=0

%o while n<50:

%o L.append(round(numerical_approx((n+n/11))*3600))

%o n+=1

%o print(L)

%Y Cf. A120500 (as HHMMSS).

%K nonn

%O 0,2

%A _Sean Lestrange_, Aug 14 2020

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Last modified April 21 00:22 EDT 2024. Contains 371850 sequences. (Running on oeis4.)