A045516 Factorials with initial digit '4'.

40320, 479001600, 403291461126605635584000000, 4274883284060025564298013753389399649690343788366813724672000000000000, 40526919504877216755680601905432322134980384796226602145184481280000000000000

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base

Comments

Benford's law shows that this sequence will contain about (log 5 - log 4)/log 10 =~ 10% of factorials. [Charles R Greathouse IV, Nov 13 2010]

The next term (a(6)) has 106 digits. - Harvey P. Dale, Nov 05 2015

Links

• Index entries for sequences related to Benford's law

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529.

Cf. A000142.

Programs

Mathematica

Select[Range[200]!,IntegerDigits[#][[1]]==4&] (* Harvey P. Dale, Nov 05 2015 *)

Formula

a(n) = A000142(A045523(n)). - Amiram Eldar, Jul 19 2020

Extensions

One more term (a(5)) from Harvey P. Dale, Nov 05 2015