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Search: id:A144049
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| A144049 |
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Number of different cycles of digits in the hexadecimal (base-16) expansions of 1/p, 2/p, ..., (p-1)/p where p = n-th prime different from 2. |
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+0
1
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| 2, 4, 2, 2, 4, 8, 2, 2, 4, 6, 4, 8, 6, 2, 4, 2, 4, 2, 2, 8, 2, 2, 8, 8, 4, 2, 2, 12, 16, 18, 2, 8, 2, 4, 10, 12, 2, 2, 4, 2, 4, 2, 8, 4, 2, 2, 6, 2, 12, 8, 2, 40, 10, 64, 2, 4, 2, 12, 8, 6, 4
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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For n=3, p=7. 1/7 in hexadecimal = 0.249249249... with a period of 3. (p-1)/3 = 2. a(3)=2.
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PROGRAM
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Microsoft C#.NET: public static void Main() { int b = 16; for( int n = 3; n < 300; n += 2 ) { if( !IsPrime( n ) ) { continue; } if( b % n == 0 ) { continue; } int t = 0; int x = 1; while( true ) { t++; x *= b; int d = x / n; x %= n; if( x == 1 ) { break; } } Console.Write( (double)(n-1) / t ); Console.Write(", "); } } private static bool IsPrime( int n ) { if( n % 2 == 0 ) { return false; } int test = (int)Math.Floor( Math.Sqrt( n ) ); test -= ( 1 - test % 2 ); while( test >= 3 ) { if( n % test == 0 ) { return false; } test--; } return true; }
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CROSSREFS
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A006556 for a similar sequence using decimal expansions.
Sequence in context: A013604 A021809 A117007 this_sequence A058384 A055097 A054507
Adjacent sequences: A144046 A144047 A144048 this_sequence A144050 A144051 A144052
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KEYWORD
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easy,nonn
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AUTHOR
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Phil Scovis (phildonnia(AT)yahoo.com), Sep 08 2008
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