MathDB
2024 Alg/NT Problem 4

Source:

April 14, 2024
number theory

Problem Statement

For positive integer nn, let f(n)f(n) be the largest integer kk such that k!≤nk!\leq n, let g(n)=n−(f(n))!g(n)=n-(f(n))!, and for j≥1j\geq 1 let gj(n)=g(…(g(n))… )⏟j times.g^j(n)=\underbrace{g(\dots(g(n))\dots)}_{\text{$j$ times}}. Find the smallest positive integer nn such that gj(n)>0g^{j}(n)> 0 for all j<30j<30 and g30(n)=0g^{30}(n)=0.
Proposed by Connor Gordon
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