%I #22 Jan 05 2025 19:51:35

%S 0,1,5,15,19,22,25,27,35,37,42,45,48,51,55,59,63,64,69,70,76,77,78,88,

%T 89,90,91,92,93,94,95,104,105,106,107,108,109,110,111,112,123,124,125,

%U 132,133,134,140,141,146,147,152,157,158,162,167,171,175,176,179,183

%N Numbers k such that k! has initial digit '1'.

%C The asymptotic density of this sequence is log_10(2) = 0.301029... (A007524) (Kunoff, 1987). - _Amiram Eldar_, Jul 17 2020

%H Chai Wah Wu, <a href="/A045520/b045520.txt">Table of n, a(n) for n = 1..10000</a>

%H Sharon Kunoff, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/25-4/kunoff.pdf">N! has the first digit property</a>, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367.

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%F A008905(a(n)) = 1. - _Amiram Eldar_, Jul 17 2020

%e 0 is a term since 0! = 1 has the initial digit 1.

%t Select[ Range[ 0, 200 ], IntegerDigits[ #! ][ [ 1 ] ] == 1 & ]

%o (PARI) isok(n) = digits(n!)[1] == 1; \\ _Michel Marcus_, Feb 07 2017

%Y 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. See also A000142, A007524, A008905.

%K nonn,base

%O 1,3

%A _Jeff Burch_