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A236839
Numbers that occur as results of downward remultiplication (N -> GF(2)[X]) of some number and have at least one irreducible polynomial factor encoded by a composite number.
4
43, 79, 86, 89, 125, 135, 149, 158, 172, 178, 181, 209, 227, 235, 250, 263, 270, 281, 293, 298, 311, 316, 317, 331, 344, 349, 356, 362, 371, 383, 393, 399, 401, 418, 421, 443, 447, 454, 470, 479, 493, 500, 509, 519, 521, 523, 526, 540, 547, 562, 567, 577, 586, 596, 609
OFFSET
1,1
COMMENTS
Terms of A236841 that are found in A236838.
LINKS
EXAMPLE
43, which is A234741(43), and 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.
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A236839 (COMPOSE A236841 (MATCHING-POS 1 2 (lambda (n) (any (lambda (p) (= 1 (A066247 p))) (GF2Xfactor (A236841 n)))))))
CROSSREFS
Setwise difference A236838 \ A236834, and also A236841 \ A236850.
Sequence in context: A238248 A121957 A118075 * A183074 A289730 A045238
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 02 2014
STATUS
approved