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

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

Offset

1,3

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)

Links

Table of n, a(n) for n=1..10.

Vaclav Kotesovec, a(11)-a(14)

Example

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

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

Crossrefs

Cf. A000142, A034886.

Sequence in context: A101135 A280054 A088220 * A085612 A073915 A076381

Adjacent sequences: A333428 A333429 A333430 * A333432 A333433 A333434

Keyword

nonn,base

Author

Robert G. Wilson v, Mar 20 2020

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

Status

approved