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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 (list; graph; refs; listen; history; text; internal format)
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^(i-1), 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

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Last modified December 10 12:43 EST 2019. Contains 329896 sequences. (Running on oeis4.)