McCarthy 91 function

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

The McCarthy 91 function is defined as

${\displaystyle M(n)=\left\{{\begin{matrix}n-10,&{\mbox{if }}n>100{\mbox{ }}\\M(M(n+11)),&{\mbox{if }}n\leq 100{\mbox{ }}\end{matrix}}\right.}$

Examples:

M(99) = M(M(110)) since 99 ${\displaystyle \leq }$ 100
      = M(100) since 110 > 100
      = M(M(111)) since 100 ${\displaystyle \leq }$ 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