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a(n) = leading digit of n! in base 16.
14

%I #26 Jan 15 2021 16:35:43

%S 1,1,2,6,1,7,2,1,9,5,3,2,1,1,1,1,1,1,1,1,2,2,3,5,8,12,1,2,3,6,13,1,3,

%T 6,13,1,4,9,1,3,8,1,3,10,1,4,14,2,7,1,4,14,2,9,2,7,1,5,1,4,1,4,1,3,15,

%U 4,1,4,1,5,1,6,1,7,2,10,3,15,4,1,7,2,11,3,1,6,2,11,4,1,7,2,1,5,2,12,4,1,11

%N a(n) = leading digit of n! in base 16.

%H David A. Corneth, <a href="/A136766/b136766.txt">Table of n, a(n) for n = 0..9999</a> (first 1001 terms from Robert G. Wilson v)

%e For n=5, 5! = 5*4*3*2*1 = 120 in base 10, which is 78 in hexadecimal (7*16 + 8*1), so a(5) = 7. - _Michael B. Porter_, Sep 20 2016

%t Array[ IntegerDigits[#!, 16][[1]] &, 1001, 0] (* _Robert G. Wilson v_, Sep 20 2016 *)

%t Table[Floor[#/16^Floor@ Log[16, #]] &[n!], {n, 0, 98}] (* _Michael De Vlieger_, Sep 20 2016 *)

%o (PARI) a(n) = digits(n!, 16)[1]; \\ _Michel Marcus_, Jan 27 2015

%Y Cf. A000142, A136702, A136754, A136755, A136756, A136757, A136758, A136759, A136760, A008905, A136761, A136762, A136763, A136764, A136765.

%K nonn,easy,base

%O 0,3

%A _Carl R. White_, Jan 21 2008