OFFSET
1,1
COMMENTS
Is every prime present?
Yes, see the Filaseta reference. - Thomas Ordowski, Feb 19 2014
Corresponding evaluation at x=10 is A206073. - Michael Somos, Feb 26 2014
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..21692
John Brillhart, Michael Filaseta, Andrew Odlyzko, On an irreducibility theorem of A. Cohn, Canad. J. Math. 33(1981), pp. 1055-1059.
Michael Filaseta, A further generalization of an irreducibility theorem of A. Cohn, Canad J. Math. 34 (1982), pp. 1390-1395.
FORMULA
Other identities and observations. For all n >= 1:
A255574(a(n)) = n.
EXAMPLE
(See the example at A206073.)
MATHEMATICA
t = Table[IntegerDigits[n, 2], {n, 1, 850}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
Table[p[n, x], {n, 1, 15}]
u = {}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]],
AppendTo[u, n]], {n, 300}];
u (* A206074 *)
Complement[Range[200], u] (* A205783 *)
b[n_] := FromDigits[IntegerDigits[u, 2][[n]]]
Table[b[n], {n, 1, 40}] (* A206073 *)
PROG
(PARI) for(n=2, 10^3, if( polisirreducible( Pol(binary(n)) ), print1(n, ", ") ) ); \\ Joerg Arndt, Feb 19 2014
CROSSREFS
Cf. A206073, A205783 (complement), A206075 (nonprime terms), A014580 (irreducible over GF(2), a subsequence of this one), A000040 (primes, also a subsequence), A260427 (terms that are reducible over GF(2)).
Cf. A255574 (left inverse).
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 03 2012
EXTENSIONS
Clarified name, added more terms, Joerg Arndt, Feb 20 2014
STATUS
approved