A086654 Smallest number a(n) > n such that a(n)! contains n! as a substring.

1, 5, 4, 9, 20, 14, 40, 28, 434, 10, 1337, 354, 5370, 6180, 179472

Offset: 0

Author

Erich Friedman, Sep 11 2003

Keywords

• nonn
• base
• hard
• more

Comments

From Michael S. Branicky, Apr 11 2025: (Start)

500000 < a(15..20), with lower values ruled out by exhaustive search;

a(16) <= 80377420, a(17) <= 5770007, a(18) <= 674238256, with upper bound k achieved where A004154(k) ends with A004154(n). (End)

Examples

			a[5]=14 since 14!= 8717829_120_0.
		

Crossrefs

Cf. A004154

Formula

a(10^m-1) = 10^m, m >= 0. - Michael S. Branicky, Apr 10 2025

Extensions

a(13)-a(14) from Michael S. Branicky, Apr 10 2025