login
A217460
Odd values of n such that the polynomial 1+x+x^2+...+x^(n-1) is reducible over GF(2).
1
7, 9, 15, 17, 21, 23, 25, 27, 31, 33, 35, 39, 41, 43, 45, 47, 49, 51, 55, 57, 63, 65, 69, 71, 73, 75, 77, 79, 81, 85, 87, 89, 91, 93, 95, 97, 99, 103, 105, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 133, 135, 137, 141, 143, 145, 147, 151, 153, 155, 157, 159, 161, 165, 167, 169, 171, 175, 177, 183, 185, 187, 189, 191, 193, 195, 199
OFFSET
1,1
COMMENTS
This sequence is the union of the odd composite numbers and the primes for which 2 is not a primitive root.
LINKS
MATHEMATICA
nn = 200; Union[Select[Range[3, nn, 2], ! PrimeQ[#] &], Select[Prime[Range[2, PrimePi[nn]]], PrimitiveRoot[#] =!= 2 &]] (* T. D. Noe, Sep 19 2012 *)
PROG
(PARI) for(i=4, 200, if(isprime(i), if(znorder(Mod(2, i))!=(i-1), print(i)), if(i%2==1, print(i))))
(PARI) for(i=0, 200, i++; if(matsize(factormod((x^i+1)/(x+1), 2, 1))[1]>1, print(i)))
CROSSREFS
KEYWORD
nonn
AUTHOR
V. Raman, Oct 04 2012
STATUS
approved