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A014580
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Binary irreducible polynomials (primes in ring GF(2)[X]), evaluated at X=2.
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33
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2, 3, 7, 11, 13, 19, 25, 31, 37, 41, 47, 55, 59, 61, 67, 73, 87, 91, 97, 103, 109, 115, 117, 131, 137, 143, 145, 157, 167, 171, 185, 191, 193, 203, 211, 213, 229, 239, 241, 247, 253, 283, 285, 299, 301, 313, 319, 333, 351, 355, 357, 361, 369, 375
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OFFSET
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1,1
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COMMENTS
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Or, binary irreducible polynomials, interpreted as binary vectors, then written in base 10.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1377 (through degree 13)
Index entries for sequences operating on GF(2)[X]-polynomials
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EXAMPLE
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x^4 + x^3 + 1 -> 16+8+1 = 25. Or, x^4 + x^3 + 1 -> 11001 (binary) = 25 (decimal).
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MATHEMATICA
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fQ[n_] := Block[{ply = Plus @@ (Reverse@ IntegerDigits[n, 2] x^Range[0, Floor@ Log2@ n])}, ply == Factor[ply, Modulus -> 2] && n != 2^Floor@ Log2@ n]; fQ[2] = True; Select[ Range@ 378, fQ] (* Robert G. Wilson v, Aug 12 2011 *)
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PROG
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(PARI) is(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)) \\ Charles R Greathouse IV, Mar 22 2013
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CROSSREFS
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Cf. A000031, A001037, A048720. Written in binary: A058943.
Characteristic function: A091225. Inverse: A091227. a(n) = A091202(A000040(n)). Almost complement of A091242. Union of A091206 & A091214 and also of A091250 & A091252. First differences: A091223. Apart from a(1) and a(2), a subsequence of A092246 and hence A000069.
Sequence in context: A145673 A040116 A155153 * A197227 A091206 A038963
Adjacent sequences: A014577 A014578 A014579 * A014581 A014582 A014583
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KEYWORD
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nonn
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AUTHOR
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David Petry (petry(AT)accessone.com)
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STATUS
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approved
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