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%I #7 Oct 13 2013 03:03:08
%S 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,
%T 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
%N 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.
%e For n=3, p=7. 1/7 in hexadecimal = 0.249249249... with a period of 3. (p-1)/3 = 2. a(3)=2.
%o (C#.NET)
%o 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; }
%Y A006556 for a similar sequence using decimal expansions.
%K easy,nonn,base
%O 1,1
%A _Phil Scovis_, Sep 08 2008
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