A136416 Numbers n such that 1+(x+1)^k+(x+1)^n is a primitive polynomial over GF(2) for some k where 0<k<n.

2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 15, 17, 18, 20, 21, 22, 23, 25, 28, 29, 31, 33, 35, 36, 39, 41, 42, 47, 49, 52, 54, 55, 57, 58, 60, 62, 63, 65, 66, 68, 71, 73, 74, 76, 79, 81, 84, 86, 87, 89, 92, 93, 94, 95, 97, 98, 100, 102, 103, 105, 106, 108, 110, 111, 113, 118, 119, 121

Offset

1,1

Comments

Iff the trinomial T(x)=1+x^k+x^n is irreducible (A073571) then the polynomial T(x+1)=1+(x+1)^k+(1+x)^n is irreducible.

The order of T(x+1) is in general different from the order of T(x).

So this sequence is different from A073726: for example, 1+(x+1)^7+(1+x)^10 is primitive but 1+(x+1)^3+(1+x)^10 is not (while 1+x^7+x^10 and 1+x^3+x^10 are mutual reciprocal and have the same order).

Links

Joerg Arndt, Mar 31 2008, Table of n, a(n) for n = 1..211

Joerg Arndt, Matters Computational (The Fxtbook)

Example

10 is in the sequence because 1+(x+1)^7+(1+x)^10 is a primitive polynomial over GF(2).

Crossrefs

Sequence in context: A328242 A294295 A191852 * A072497 A300064 A039217

Adjacent sequences: A136413 A136414 A136415 * A136417 A136418 A136419

Keyword

nonn

Author

Joerg Arndt, Mar 31 2008, May 02 2009

Status

approved