The McCarthy 91 function is defined as
Examples:
M(99) = M(M(110)) since 99 <math>\le</math> 100 = M(100) since 110 > 100 = M(M(111)) since 100 <math>\le</math> 100 = M(101) since 111 > 100 = 91 since 101 > 100
M(87) = M(M(98)) = M(M(M(109))) = M(M(99)) = M(M(M(110))) = M(M(100)) = M(M(M(111))) = M(M(101)) = M(91) = M(M(102)) = M(92) = M(M(103)) = M(93) .... Pattern continues = M(99) (same as above proof) = 91
Here's a sample McCarthy 91 program in Java:
public class McCarthy extends Object { static int count = 1;
public McCarthy() { }
public int Mc91(int n) { count = count + 1;
System.out.println("Number after " + count + " iteration(s): " + n); if ( n < 0 ) { System.out.println("\n Not a positive integer"); System.exit(1); }
if ( n > 100 ) { return n10; }
if ( n < 101 ) { return Mc91(Mc91(n+11)); }
return 0; }
public static void main(String[] args) { McCarthy yorick1 = new McCarthy(); int yorick = Integer.parseInt(args[0]); System.out.println("\n Number: " + yorick); System.out.println("Final Number: " + yorick1.Mc91(yorick)); } }
Search Encyclopedia

Featured Article
