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A256749 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.

%I A256749 #17 Jan 30 2025 11:22:21
%S A256749 0,60,61,120,122,180,183,240,244,300,305,360,366,420,427,480,488,540,
%T A256749 549,600,610,660,671,721,732,781
%N A256749 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 A256749 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 A256749 a(0) = 0 as the second-hand is over the minute-hand and the hour-hand at 0:00:00,
%e A256749 a(1) = 60 as the second-hand is over the hour-hand at 0:01:00,
%e A256749 a(2) = 61 as the second-hand is over the minute-hand at 0:01:01,...
%e A256749 a(23) = 721 as the second-hand is over the hour-hand at 0:12:01.
%o A256749 (Python)
%o A256749 m0 = 0
%o A256749 s = [0]
%o A256749 for i in range(1, 60*12+1):
%o A256749     m0 += 1
%o A256749     m = m0 % 60
%o A256749     h = (m0 // 12) % 60
%o A256749     a, b = i * 60 + h, i * 60 + m
%o A256749     s.append(a)
%o A256749     s.append(b)
%o A256749 s = list(sorted(set(s)))
%o A256749 for i in range(len(s)):
%o A256749     print ('A256749('+str(i)+') = '+str(s[i]))
%K A256749 easy,nonn
%O A256749 0,2
%A A256749 _Martin Y. Champel_, Apr 09 2015