

A246156


Odd reducible polynomials over GF(2), coded in binary. (Polynomials with the constant term 1 that are reducible over GF(2)).


6



5, 9, 15, 17, 21, 23, 27, 29, 33, 35, 39, 43, 45, 49, 51, 53, 57, 63, 65, 69, 71, 75, 77, 79, 81, 83, 85, 89, 93, 95, 99, 101, 105, 107, 111, 113, 119, 121, 123, 125, 127, 129, 133, 135, 139, 141, 147, 149, 151, 153, 155, 159, 161, 163, 165, 169, 173, 175, 177, 179, 181, 183, 187, 189, 195, 197, 199, 201
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OFFSET

1,1


COMMENTS

Selfinverse permutation A193231 maps each term of this sequence to some term of A246158 and vice versa.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..13846
Index entries for sequences operating on GF(2)[X]polynomials


EXAMPLE

5, which is 101 in binary, encodes polynomial x^2 + 1, which factorizes as (x+1)(x+1) over GF(2), (5 = A048720(3,3)), thus it is reducible in that polynomial ring. Also, its constant term is 1, (not zero), thus 5 is a member of this sequence.


MAPLE

filter:= proc(n) local L, p, x;
L:= convert(n, base, 2);
p:= add(L[i]*x^(i1), i=1..nops(L));
not (Irreduc(p) mod 2)
end proc:
select(filter, [seq(2*i+1, i=1..100)]); # Robert Israel, Aug 21 2014


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A246156 (COMPOSE A091242 (MATCHINGPOS 1 1 (COMPOSE odd? A091242))))


CROSSREFS

Intersection of A091242 and A005408 (odd numbers).
A246157 is a subsequence. Cf. also A048720, A193231, A246158.
Sequence in context: A106503 A267648 A160593 * A059655 A250120 A063093
Adjacent sequences: A246153 A246154 A246155 * A246157 A246158 A246159


KEYWORD

base,nonn


AUTHOR

Antti Karttunen, Aug 20 2014


STATUS

approved



