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A129832 Integers n such that the n-th cyclotomic polynomial Phi(n) is irreducible over GF(2). 1
1, 2, 3, 5, 6, 9, 10, 11, 13, 18, 19, 22, 25, 26, 27, 29, 37, 38, 50, 53, 54, 58, 59, 61, 67, 74, 81, 83, 101, 106, 107, 118, 121, 122, 125, 131, 134, 139, 149, 162, 163, 166, 169, 173, 179, 181, 197, 202, 211, 214, 227, 242, 243, 250, 262, 269, 278, 293 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..58.

FORMULA

This sequence consists of 1, 2 and numbers having primitive root 2 (that is, numbers that are powers of primes p in sequence A001122, or twice powers of p). - T. D. Noe, Jan 03 2008

EXAMPLE

7 is absent from the list as Phi(7) == (x^3 + x + 1)*(x^3 + x^2 + 1) (mod 2).

MATHEMATICA

Select[Range[300], Transpose[Rest[FactorList[Cyclotomic[#, x], Modulus -> 2]]][[2]] == {1} &] (* T. D. Noe, Mar 03 2014 *)

PROG

(PARI) for(x=1, 200, if(polisirreducible(Mod(1, 2)*polcyclo(x)), print1(x", ")))

CROSSREFS

Sequence in context: A162923 A107040 A045989 * A166687 A189224 A018762

Adjacent sequences:  A129829 A129830 A129831 * A129833 A129834 A129835

KEYWORD

easy,nonn

AUTHOR

Phil Carmody, May 21 2007

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)