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%I #28 Dec 14 2023 05:14:08
%S 1,1,2,1,1,4,1,1,4,1,1,2,1,1,2,1,1,4,1,1,4,1,1,2,1,1,2,1,1,4,1,1,4,1,
%T 1,2,1,1,2,1,1,4,1,1,4,1,1,2,1,1,2,1,1,4,1,1,4,1,1,2,1,1,2,1,1,4,1,1,
%U 4,1,1,2,1,1,2,1,1,4,1,1,4,1,1,2,1,1,2,1,1,4,1,1,4,1,1,2,1,1,2,1,1,4,1,1,4,1,1,2
%N The exact power of 2 that divides the n-th Bell number (A000110). Has period 12.
%C { Bell(n) mod 8 } is periodic with period 24, the period being (1 1 2 5 7 4 3 5 4 3 7 2 5 5 2 1 3 4 7 1 4 7 3 2). Hence the highest power of 2 dividing a Bell number is 4. - _David W. Wilson_, Jun 29 2001
%H Amiram Eldar, <a href="/A061462/b061462.txt">Table of n, a(n) for n = 0..10000</a>
%H W. F. Lunnon et al., <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa35/aa3511.pdf">Arithmetic properties of Bell numbers to a composite modulus I</a>, Acta Arith., 35 (1979), 1-16.
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,1).
%t PadRight[{},120,{1,1,2,1,1,4,1,1,4,1,1,2}] (* _Harvey P. Dale_, Sep 24 2017 *)
%o (PARI) a(n)=[1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2][n%12+1] \\ _Charles R Greathouse IV_, Jul 13 2016
%Y Cf. A000110.
%K nonn,easy
%O 0,3
%A Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 10 2001
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