A333431 Numbers k such that k! has a factorial number of decimal digits.

0, 1, 2, 3, 4, 9, 24, 342, 11158, 145435633325318659

Offset: 1

Author

Robert G. Wilson v, Mar 20 2020

Keywords

• nonn
• base

Comments

From Vaclav Kotesovec, Mar 22 2020: (Start)

a(11) has 1199 digits and a(11)! has 525! digits.

a(12) has 1300 digits and a(12)! has 562! digits.

a(13) has 3733 digits and a(13)! has 1380! digits.

a(14) has 4730 digits and a(14)! has 1693! digits.

a(15), if it exists, must have more than 5732 digits and a(15)! must have more than 2000! digits. (End)

Examples

			9 is in the sequence since 9! = 362880 which has 6 decimal digits and 6 = 3!.
		

Links

• Vaclav Kotesovec, a(11)-a(14)

Crossrefs

Cf. A000142, A034886.

Programs

Mathematica

f = k = 1; lst = {0}; While[k < 12000, f *= k; If[ MemberQ[{1, 2, 6, 24, 120, 720, 5040, 40320, 362880}, IntegerLength@ f], AppendTo[lst, k]]; k++]; lst

Extensions

a(10) from Giovanni Resta, Mar 21 2020

a(11)-a(12) from Vaclav Kotesovec, Mar 21 2020

a(13)-a(14) from Vaclav Kotesovec, Mar 22 2020