MathDB

For positive integer

n

, let

f(n)

be the largest integer

k

such that

k!\leq n

, let

g(n)=n-(f(n))!

, and for

j\geq 1

let

g^j(n)=\underbrace{g(\dots(g(n))\dots)}_{\text{$j$ times}}.

Find the smallest positive integer

n

such that

g^{j}(n)> 0

for all

j<30

and

g^{30}(n)=0

.
Proposed by Connor Gordon

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