|
|
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
|
|
|
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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|