

A260428


Composite numbers whose binary representations encode a polynomial (with coefficients 0 or 1) which is irreducible over Q, but reducible over GF(2).


4



69, 77, 81, 121, 169, 205, 209, 261, 265, 275, 289, 295, 305, 321, 323, 327, 329, 339, 377, 405, 407, 437, 453, 473, 475, 481, 493, 517, 533, 551, 553, 559, 565, 575, 581, 583, 595, 625, 649, 667, 671, 689, 703, 707, 737, 747, 749, 755, 763, 767, 779, 781, 785, 805, 815, 833, 835, 851, 855, 861, 869, 893, 905
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OFFSET

1,1


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..11585


MAPLE

f:= proc(n) local L, p, x;
if isprime(n) then return false fi;
L:= convert(n, base, 2);
p:= add(L[i]*x^(i1), i=1..nops(L));
irreduc(p) and not (Irreduc(p) mod 2);
end proc:
select(f, [$2..10000]); # Robert Israel, Jul 27 2015


PROG

(PARI)
isA260428(n) = (polisirreducible( Pol(binary(n)) ) && !polisirreducible(Pol(binary(n))*Mod(1, 2)) && !isprime(n));
n = 0; i = 0; while(n < 65537, n++; if(isA260428(n), i++; write("b260428.txt", i, " ", n)));


CROSSREFS

Intersection of A002808 and A260427.
Intersection of A091212 and A206074.
Intersection of A091242 and A206075.
Complement of A257688 in A206074.
Sequence in context: A166067 A253437 A325386 * A168477 A264045 A295806
Adjacent sequences: A260425 A260426 A260427 * A260429 A260430 A260431


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jul 26 2015


STATUS

approved



