A144049 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.

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

Offset

1,1

Links

Table of n, a(n) for n=1..61.

Example

For n=3, p=7. 1/7 in hexadecimal = 0.249249249... with a period of 3. (p-1)/3 = 2. a(3)=2.

Prog

(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; }

Crossrefs

A006556 for a similar sequence using decimal expansions.

Sequence in context: A340129 A213433 A294354 * A368435 A058384 A255671

Adjacent sequences: A144046 A144047 A144048 * A144050 A144051 A144052

Keyword

easy,nonn,base

Author

Phil Scovis, Sep 08 2008

Status

approved