

A206074


nth irreducible polynomial over Q (with coefficients 0 or 1) evaluated at x=2.


26



2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 55, 59, 61, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 97, 101, 103, 107, 109, 113, 115, 117, 121, 127, 131, 137, 139, 143, 145, 149, 151, 157, 163, 167, 169, 171, 173, 179, 181, 185, 191, 193, 197, 199, 203, 205, 209, 211, 213, 223, 227, 229
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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. 10551059.
Michael Filaseta, A further generalization of an irreducibility theorem of A. Cohn, Canad J. Math. 34 (1982), pp. 13901395.


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).
Cf. also permutations A260421  A260426.
Disjoint union of A257688 (without 1) and A260428.
a(n) differs from A186891(n+1) for the first time at n=21, where a(21) = 67, while A186891(22) = 65, a term missing from here. There are several other sequences that do not diverge until after approx. the twentieth term from this one (see the contextlinks).
Sequence in context: A161578 A261271 A186891 * A257688 A257689 A257691
Adjacent sequences: A206071 A206072 A206073 * A206075 A206076 A206077


KEYWORD

nonn


AUTHOR

Clark Kimberling, Feb 03 2012


EXTENSIONS

Clarified name, added more terms, Joerg Arndt, Feb 20 2014


STATUS

approved



