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a(n) is the time expressed in seconds starting at 0:00:00 at which the second-hand of a classical three hands clock is passing over any of the two other hands considering the minute-hand turns of 6 degrees in one minute and the hour-hand of 6 degrees in 12 minutes.
1

%I #17 Jan 30 2025 11:22:21

%S 0,60,61,120,122,180,183,240,244,300,305,360,366,420,427,480,488,540,

%T 549,600,610,660,671,721,732,781

%N a(n) is the time expressed in seconds starting at 0:00:00 at which the second-hand of a classical three hands clock is passing over any of the two other hands considering the minute-hand turns of 6 degrees in one minute and the hour-hand of 6 degrees in 12 minutes.

%C The sequence is given for its first 1249 terms which corresponds to 12 hours. At 12:00:00 the clock is back to its initial state but as the time wheel keeps on turning a(1248) = 43200 + a(0) , a(1249) = 43200 + a(1), a(n + p*1248) = a(n) + p*43200 for any nonnegative integer p.

%e a(0) = 0 as the second-hand is over the minute-hand and the hour-hand at 0:00:00,

%e a(1) = 60 as the second-hand is over the hour-hand at 0:01:00,

%e a(2) = 61 as the second-hand is over the minute-hand at 0:01:01,...

%e a(23) = 721 as the second-hand is over the hour-hand at 0:12:01.

%o (Python)

%o m0 = 0

%o s = [0]

%o for i in range(1, 60*12+1):

%o m0 += 1

%o m = m0 % 60

%o h = (m0 // 12) % 60

%o a, b = i * 60 + h, i * 60 + m

%o s.append(a)

%o s.append(b)

%o s = list(sorted(set(s)))

%o for i in range(len(s)):

%o print ('A256749('+str(i)+') = '+str(s[i]))

%K easy,nonn,changed

%O 0,2

%A _Martin Y. Champel_, Apr 09 2015