A236849 -id:A236849 - cp's OEIS frontend

A236834 Numbers that do not occur as results of "downward" remultiplication (N -> GF(2)[X]) of any number; numbers not present in A234741.

25, 50, 55, 87, 91, 100, 110, 115, 117, 133, 143, 145, 159, 171, 174, 182, 185, 200, 203, 213, 220, 230, 234, 237, 247, 249, 253, 266, 267, 279, 285, 286, 290, 299, 301, 318, 319, 321, 333, 339, 342, 345, 348, 351, 355, 357, 361, 364, 369, 370, 375, 385, 391, 395, 400

Offset: 1

Antti Karttunen, Jan 31 2014

nonn

Numbers that do not occur in A234741 (A236841).
This is a subsequence of A236838, thus all terms are GF(2)[X]-multiples of some of the terms of A091214. (Cf. also A236844).
a(5)=91 is the first term that does not occur in A236849. On the other hand, A236849(4)=75, is the first term in the latter which does not occur here.

Antti Karttunen, Table of n, a(n) for n = 1..2525

Complement: A236841. This sequence is a setwise difference of A236838 and A236839.
A091214 is a subsequence.
Positions of zeros in A236833, A236836, A236837 and A236861
Cf. also A236844, A234741, A236835.

A236844 Numbers that do not occur as results of "upward" remultiplication (GF(2)[X] -> N) of any number; numbers not present in A234742.

Original entry on oeis.org

5, 10, 15, 17, 20, 23, 29, 30, 34, 35, 40, 43, 45, 46, 51, 53, 58, 60, 65, 68, 69, 70, 71, 79, 80, 83, 85, 86, 89, 90, 92, 95, 101, 102, 105, 106, 107, 113, 116, 119, 120, 125, 127, 129, 130, 135, 136, 138, 139, 140, 142, 149, 151, 153, 155, 158, 159, 160, 161

Offset: 1

Antti Karttunen, Jan 31 2014

nonn

Numbers that do not occur in A234742 (A236842).
This is a subsequence of A236848, thus all terms are divisible by at least one such prime which is reducible as polynomial over GF(2) (i.e. one of the primes in A091209).
A236835(7)=27 is the first member of A236835 which does not occur here. a(12)=43 is the first term here which does not occur in A236835.

Antti Karttunen, Table of n, a(n) for n = 1..19282

Complement: A236842.
A setwise difference of A236848 and A236849.
A091209 is a subsequence.
Positions of zeros in A236853, A236846, A236847 and A236862.
Cf. A236845.
Cf. also A236834.

For all n, A236379(a(n)) > 0.

A236848 Numbers that have at least one prime divisor encoding a reducible polynomial in ring GF(2)[X]; multiples of terms of A091209.

Original entry on oeis.org

5, 10, 15, 17, 20, 23, 25, 29, 30, 34, 35, 40, 43, 45, 46, 50, 51, 53, 55, 58, 60, 65, 68, 69, 70, 71, 75, 79, 80, 83, 85, 86, 87, 89, 90, 92, 95, 100, 101, 102, 105, 106, 107, 110, 113, 115, 116, 119, 120, 125, 127, 129, 130, 135, 136, 138, 139, 140, 142, 145, 149, 150

Offset: 1

Antti Karttunen, Jan 31 2014

nonn

Numbers that are divisible by at least one prime whose binary representation encodes a polynomial which is reducible in polynomial ring GF(2)[X].

Antti Karttunen, Table of n, a(n) for n = 1..12311

Disjoint union of A236844 and A236849.
Complement: A236860.
Cf. A091209, A236838.

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.

Original entry on oeis.org

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

Antti Karttunen, Feb 02 2014

nonn

Terms of A236841 that are found in A236838.

			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.

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

Setwise difference A236838 \ A236834, and also A236841 \ A236850.

Cf. A236838, A236841, A236849.

cp's OEIS Frontend

A236834 Numbers that do not occur as results of "downward" remultiplication (N -> GF(2)[X]) of any number; numbers not present in A234741.

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A236844 Numbers that do not occur as results of "upward" remultiplication (GF(2)[X] -> N) of any number; numbers not present in A234742.

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A236848 Numbers that have at least one prime divisor encoding a reducible polynomial in ring GF(2)[X]; multiples of terms of A091209.

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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.

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