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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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1
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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, 4, 24, 48, 4, 8, 6, 4, 5, 54, 4, 6, 5, 4, 30, 60, 4, 62, 32, 4, 5, 6, 4
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OFFSET
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4,1
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COMMENTS
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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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LINKS
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FORMULA
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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 gcd(50-1, 400-1) = 8 - 1 = 7.
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MAPLE
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A090370:=proc(n) local m; m:=4; while (gcd(n-1, m*n - 1) <> m-1) do m:=m+1; end; return m; end; # Søren Eilers, Aug 09 2018
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MATHEMATICA
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a[n_] := Block[{m=4}, While[GCD[n-1, n*m-1] != m-1, m++]; m]; Table[a[k], {k, 4, 67}] (* Giovanni Resta, Aug 09 2018 *)
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PROG
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(PARI) a(n) = {m = 4; while (gcd(n-1, m*n - 1) != m-1, m++); return (m); } \\ Michel Marcus, Jul 27 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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