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A169912 Number of irreducible Boolean polynomials of degree n. 5
1, 2, 1, 3, 5, 9, 19, 39, 77, 168, 323, 682, 1424, 2902, 5956, 12368, 25329, 51866, 106427, 217216, 442313, 902921, 1833029, 3719745, 7548521, 15264350, 30859444, 62355854, 125773168, 253461052, 510471015, 1027067090, 2065390101, 4151081457, 8336751732, 16734781946, 33583213577, 67357328359, 135056786787 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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].

The subsequence of primes begins: 2, 3, 5, 19, 106427, no more through a(38). [Jonathan Vos Post, Jan 28 2011]

LINKS

Table of n, a(n) for n=0..38.

Index entries for sequences related to carryless arithmetic

EXAMPLE

a(0) = 1: 1.

a(1) = 2: X and X+1.

a(2) = 1: X^2+1 (note that X^2+X+1 = (X+1)^2 is reducible).

a(3) = 3: X^3+1, X^3+X+1, X^3+X^2+1.

CROSSREFS

a(n) + A169913(n) = 2^n.

Cf. A001037, A169913, A169914.

Sequence in context: A021828 A094341 A255939 * A092944 A049902 A096631

Adjacent sequences:  A169909 A169910 A169911 * A169913 A169914 A169915

KEYWORD

nonn,nice

AUTHOR

David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 11 2010

EXTENSIONS

More terms from David Applegate, Jul 19 2010

STATUS

approved

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Last modified July 27 02:39 EDT 2017. Contains 289840 sequences.