A045522 - OEIS

%I #21 Jan 05 2025 19:51:35

%S 9,10,11,17,28,36,41,50,62,67,74,83,84,116,117,127,128,136,143,149,

%T 154,164,173,177,181,192,199,202,229,245,250,255,260,267,274,283,285,

%U 296,298,300,332,334,336,349,358,360,367,374,381,386,411,416,424,435,449

%N Numbers k such that k! has initial digit '3'.

%C The asymptotic density of this sequence is log_10(4/3) = 0.124938... (Kunoff, 1987). - _Amiram Eldar_, Jul 17 2020

%H Chai Wah Wu, <a href="/A045522/b045522.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)) = 3. - _Amiram Eldar_, Jul 17 2020

%e 9 is a term since 9! = 362880 has the initial digit 3.

%t Select[ Range[ 500 ], IntegerDigits[ #! ] [ [ 1 ] ] == 3 & ]

%o (PARI) isok(n) = digits(n!)[1] == 3; \\ _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, A008905.

%K nonn,base

%O 1,1

%A _Jeff Burch_