MathDB

Let

N_9

be the answer to problem 9.
In a rainforest, there is a row of nine rocks labeled from

1

N_9

. A gecko is standing on rock

1

. The gecko jumps according to following rules:
[*] if it is on rock

1

, then it will jump with equal probability to any of the other rocks. [*] if it is on rock

R

and

R

is prime, then it will jump to rock

N_9

. [*] if it is on rock

4

, then it will jump with equal probability to rock

1

or rock

6

. [*] if it is on rock

R

and

R

is composite with

4<R<N_9

, then it will jump with equal probability to rock

Q

S

, where

Q

is the greatest composite number less than

R

, and

S

is the smallest composite number greater than

R

. [*] if it is on rock

N_9

, then it stops jumping.
The expected number of jumps the gecko will take to reach rock

N_9

\tfrac{p}{q}

, where

p

are

q

relatively prime positive integers. Compute

p+q

Problem Statement