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A236838
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Numbers whose binary representation encodes a polynomial over GF(2) with the property that at least one of its irreducible factors is encoded by a composite number.
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5
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25, 43, 50, 55, 79, 86, 87, 89, 91, 100, 110, 115, 117, 125, 133, 135, 143, 145, 149, 158, 159, 171, 172, 174, 178, 181, 182, 185, 200, 203, 209, 213, 220, 227, 230, 234, 235, 237, 247, 249, 250, 253, 263, 266, 267, 270, 279, 281, 285, 286, 290, 293, 298, 299
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OFFSET
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1,1
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COMMENTS
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In the range 1..10000 about half of the natural numbers seem to be in this set, and the terms are getting more frequent, although rather slowly. (Please see the graph.)
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LINKS
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EXAMPLE
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25, in binary '11001', encodes polynomial x^4 + x^3 + 1, which is irreducible in polynomial ring GF(2)[X], but is composite in N, thus it is a term of this sequence.
43, in binary '101011', encodes polynomial x^5 + x^3 + x + 1, which factors as (x + 1)(x^4 + x^3 + 1), i.e., 43 = A048720(3,25), and the latter factor of these, encoded by 25, is a composite in N, thus 43 is a term of this sequence.
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PROG
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(Scheme) (define A236838 (MATCHING-POS 1 1 (lambda (n) (any (lambda (p) (= 1 (A066247 p))) (GF2Xfactor n)))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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