A132454 First primitive GF(2)[X] polynomials of degree n and minimal number of terms, expressed as -k for X^n+X^k+1, else with X^n suppressed.

1, -1, -1, -1, -2, -1, -1, 29, -4, -3, -2, 83, 27, 43, -1, 45, -3, -7, 39, -3, -2, -1, -5, 27, -3, 71, 39, -3, -2, 83, -3, 197, -13, 281, -2, -11, 83

Offset: 1

Author

Francois R. Grieu, Aug 22 2007

Keywords

• more
• sign

Comments

More precisely: when there exists k, 0

Examples

			a(10)=-3, representing the GF(2)[X] polynomial X^10+X^3+1, because this degree 10 trinomial is primitive, contrary to X^10+X^1+1, X^10+X^2+1 and X^10+X^2+X^1.
		

Links

• Index entries for sequences operating on GF(2)[X]-polynomials
• Index entries for sequences related to trinomials over GF(2)

Crossrefs

Either of 2^n+2^(-a(n))+1 or 2^n+a(n) belongs to A091250. If there exists m such that n = A073726(m), then a(n) = -A074744(m); otherwise a(n) = A132450(n). A132453(n) gives the primitive polynomial corresponding to a(n). Cf. A132448, similar, with no restriction on number of terms. Cf. A132450, similar, with restriction to at most 5 terms. Cf. A132452, similar, with restriction to exactly 5 terms.

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