A045510 Factorials having initial digit '2'.

2, 24, 20922789888000, 2432902008176640000, 25852016738884976640000, 265252859812191058636308480000000, 263130836933693530167218012160000000

Offset

1,1

Comments

Benford's law shows that this sequence will contain about (log 3 - log 2)/log 10 =~ 18% of factorials. - Charles R Greathouse IV, Nov 13 2010

(10^10)! = 2.3257962...*10^95657055186 and (10^1000)! = 2.101826996...*10^L, with L = A034886(10^1000)-1, are both in this sequence; see also A045521. - M. F. Hasler, Apr 03 2026

Links

Table of n, a(n) for n=1..7.

Formula

a(n) = A000142(A045521(n)). - Amiram Eldar, Jul 19 2020

Mathematica

Select[Range[50]!, IntegerDigits[#][[1]]==2&] (* Harvey P. Dale, Mar 21 2020 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (digits(n!)[1] == 2, print1(n!, ", ")); ); } \\ Michel Marcus, Dec 13 2017

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.

Sequence in context: A159932 A100010 A319761 * A226325 A065665 A321350

Adjacent sequences: A045507 A045508 A045509 * A045511 A045512 A045513

Keyword

nonn,base

Author

Jeff Burch

Status

approved