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Search: id:A090370
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| A090370 |
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Least m>3 such that gcd(n-1,m*n - 1)=m-1. |
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+0
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| 4, 5, 6, 4, 8, 5, 4, 6, 12, 4, 14, 8, 4, 5, 18, 4, 20, 5, 4, 12, 24, 4, 6, 14, 4, 5, 30, 4, 32, 5, 4, 18, 6, 4, 38, 20, 4, 5, 42, 4, 44, 5, 6, 24, 48, 5, 8, 6, 4, 5, 54, 4, 6, 5, 4, 30, 60, 4, 62, 32, 4, 5, 6, 4
(list; graph; listen)
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OFFSET
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4,1
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COMMENT
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Choosing a pair (m, n) so as to redefine 1 hour=m*n minutes and 1 minute=m*n seconds, then the three hands of a fictitious n-hour clock coincide in exactly m-1 equally spaced positions, including that of the n o'clock position. For instance, in the cases where we select (m, n) as (6, 11), (8, 15), (4, 25), with m*n respectively equal to 66, 120, 100(implying 1 hour=66 minutes, 1 minute=66 seconds;1 hour=120 minutes, 1 minute=120 seconds;1 hour=100 minutes, 1 minute=100 seconds), the hands coincide in exactly 6-1=5, 8-1=7, 4-1=3 equally spaced positions on a 11-hour, 15-hour, 25-hour clock respectively.
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FORMULA
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a(n)=1+A090368(k-1) for n=2k. a(n)=1+A090369(k) for n=2k+1.
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EXAMPLE
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We have a(50)=8 because 50*8=400 is the least multiple of 50 such that (50-1,400-1)=8-1=7.
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CROSSREFS
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Cf. A090368, A090369.
Sequence in context: A010665 A096291 A016719 this_sequence A002129 A113184 A136004
Adjacent sequences: A090367 A090368 A090369 this_sequence A090371 A090372 A090373
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Nov 27 2003
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