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Number of binary digits in (n!)!.
3

%I #16 Oct 27 2021 21:52:54

%S 1,1,2,10,80,661,5802,54725,558704,6178565,73840164,950331113,

%T 13121175977,193618002604,3042570732326,50747501675076,

%U 895651186352884,16679929313440954,326936145826028780,6728526339596831313,145085354333183129464,3271200076443827203823

%N Number of binary digits in (n!)!.

%H Jon E. Schoenfield, <a href="/A152168/b152168.txt">Table of n, a(n) for n = 0..30</a>

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

%e (3!)! = 6! = 720 has ten binary digits (1011010000), so a(3) = 10.

%o (PARI) a(n) = length(binary(n!!)) \\ _Michel Marcus_, Jun 02 2013

%Y Cf. A000197, A072831.

%K base,nonn

%O 0,3

%A _Jon E. Schoenfield_, Nov 27 2008