McCarthy 91 function: Meaning (information, definition, explanation, facts)

In discrete mathematics, the McCarthy 91 function is a recursive function which takes the value 91 for all positive integers less than 102. It was conceived by computer scientist John McCarthy.

The McCarthy 91 function is defined as

Examples:

M(99) = M(M(110)) since 99 100 = M(100) since 110 > 100 = M(M(111)) since 100 100 = 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 n-10; }

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)); } }