A080308 Non-multiples of Fermat numbers 2^(2^n)+1.

1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 22, 23, 26, 28, 29, 31, 32, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 56, 58, 59, 61, 62, 64, 67, 71, 73, 74, 76, 77, 79, 82, 83, 86, 88, 89, 91, 92, 94, 97, 98, 101, 103, 104, 106, 107, 109, 112, 113, 116, 118, 121, 122, 124, 127, 128, 131

Offset

1,2

Comments

Complement of A080307. A080307 and A080308 each comprise one-half of the integers; see A080307.

It appears that the first 128 terms of this sequence constitute all of the primitive elements of GF(256) if each term is the exponent of the minimum primitive element for the irreducible polynomial splitting GF(2). For example, when GF(2) is split by F(x) = x^8 + x^4 + x^3 + x + 1, the minimum primitive element is a = x + 1. Then the primitive elements of the finite field are a^1, a^2, a^4, a^7, ... - Cody Planteen, Jul 27 2019

Links

Table of n, a(n) for n=1..66.

C. Planteen, Primitive elements and irreducible polynomials of GF(256)

Crossrefs

Cf. A000215, A080307.

Sequence in context: A344602 A333975 A140137 * A089559 A165741 A238989

Adjacent sequences: A080305 A080306 A080307 * A080309 A080310 A080311

Keyword

easy,nonn

Author

Matthew Vandermast, Feb 16 2003

Status

approved