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%I #22 Jan 05 2025 19:51:35
%S 8,12,26,53,57,73,82,118,129,155,160,169,185,212,215,218,232,240,265,
%T 272,281,294,338,351,369,376,388,393,398,403,408,421,432,443,446,482,
%U 485,498,515,522,533,544,548,576,580,593,602,616,621,641,646,657,668
%N Numbers k such that k! has initial digit '4'.
%C The asymptotic density of this sequence is log_10(5/4) = 0.096910... (Kunoff, 1987). - _Amiram Eldar_, Jul 17 2020
%H Chai Wah Wu, <a href="/A045523/b045523.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)) = 4. - _Amiram Eldar_, Jul 17 2020
%e 8 is a term since 8! = 40320 has the initial digit 4.
%t Select[ Range[ 700 ], IntegerDigits[ #! ] [[ 1 ]] == 4 & ]
%o (PARI) isok(n) = digits(n!)[1] == 4; \\ _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_