cp's OEIS Frontend

A205783 Complement of A206074, a coding of reducible polynomials over Q (with coefficients 0 or 1).

%I A205783 #23 Aug 02 2015 17:51:58
%S A205783 1,4,6,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,33,34,35,36,
%T A205783 38,39,40,42,44,45,46,48,49,50,51,52,54,56,57,58,60,62,63,64,65,66,68,
%U A205783 70,72,74,75,76,78,80,82,84,85,86,88,90,92,93,94,95,96,98,99,100
%N A205783 Complement of A206074, a coding of reducible polynomials over Q (with coefficients 0 or 1).
%C A205783 Reducibility here refers to the field of rational numbers.
%C A205783 Except for its initial 3, is A039004 a subsequence of A205783?
%H A205783 Antti Karttunen, <a href="/A205783/b205783.txt">Table of n, a(n) for n = 1..21951</a>
%F A205783 Other identities and observations. For all n >= 1:
%F A205783 A255573(a(n)) = n.
%e A205783 The reducible polynomials matching the first four terms:
%e A205783 1 = 1(base 2) matches 1
%e A205783 4 = 100(base 2) matches x^2
%e A205783 6 = 110(base 2) matches x^2 + x
%e A205783 8 = 1000(base 2) matches x^3
%e A205783 9 = 1001(base 2) matches x^3 + 1
%t A205783 t = Table[IntegerDigits[n, 2], {n, 1, 850}];
%t A205783 b[n_] := Reverse[Table[x^k, {k, 0, n}]]
%t A205783 p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
%t A205783 Table[p[n, x], {n, 1, 15}]
%t A205783 u = {}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]],
%t A205783 AppendTo[u, n]], {n, 300}];
%t A205783 u                          (* A206074 *)
%t A205783 Complement[Range[200], u]  (* A205783 *)
%t A205783 b[n_] := FromDigits[IntegerDigits[u, 2][[n]]]
%t A205783 Table[b[n], {n, 1, 40}]    (* A206073 *)
%o A205783 (PARI)
%o A205783 isA205783(n) = ((n > 0) && !polisirreducible(Pol(binary(n))));
%o A205783 n = 0; i = 0; while(n < 32768, n++; if(isA205783(n), i++; write("b205783.txt", i, " ", n)));
%o A205783 \\ _Antti Karttunen_, Jul 28 2015 after _Joerg Arndt_'s code for A206074.
%Y A205783 Cf. A206074 (complement), A255573 (left inverse).
%Y A205783 After 1 a subsequence of A091212 (69 is the first term missing from here).
%Y A205783 Cf. also permutations A260421 - A260426.
%K A205783 nonn
%O A205783 1,2
%A A205783 _Clark Kimberling_, Feb 03 2012