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.

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

Antti Karttunen, Table of n, a(n) for n = 1..1605

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.

Cf. A236838, A236841, A236849.

Sequence in context: A238248 A121957 A118075 * A183074 A289730 A045238

Adjacent sequences: A236836 A236837 A236838 * A236840 A236841 A236842

Keyword

nonn

Author

Antti Karttunen, Feb 02 2014

Status

approved