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%I #20 Jul 30 2022 08:17:28
%S 1,2,1,3,5,9,19,39,77,168,323,682,1424,2902,5956,12368,25329,51866,
%T 106427,217216,442313,902921,1833029,3719745,7548521,15264350,
%U 30859444,62355854,125773168,253461052,510471015,1027067090,2065390101,4151081457,8336751732,16734781946,33583213577,67357328359,135056786787
%N Number of irreducible Boolean polynomials of degree n.
%C Let B be the Boolean ring {0,1} with 0+0=0, 0+1=1+1=1, 0*0=0*1=0, 1*1=1 (0 = FALSE, 1 = TRUE, + = OR, * = AND); then a(n) = number of irreducible elements of degree n in the polynomial ring B[X].
%H Benjamin Baily, Justine Dell, Henry L. Fleischmann, Faye Jackson, Steven J. Miller, Ethan Pesikoff, and Luke Reifenberg, <a href="https://arxiv.org/abs/2111.09786">Irreducibility over the Max-Min Semiring</a>, arXiv:2111.09786 [math.CO], 2021.
%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%F a(n) + A169913(n) = 2^n.
%e a(0) = 1: 1.
%e a(1) = 2: X and X+1.
%e a(2) = 1: X^2+1 (note that X^2+X+1 = (X+1)^2 is reducible).
%e a(3) = 3: X^3+1, X^3+X+1, X^3+X^2+1.
%Y Cf. A001037, A169913, A169914.
%K nonn,nice
%O 0,2
%A _David Applegate_, _Marc LeBrun_ and _N. J. A. Sloane_, Jul 11 2010
%E More terms from _David Applegate_, Jul 19 2010
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