A048727 a(n) = Xmult(n,7) or rule150(n,1).

0, 7, 14, 9, 28, 27, 18, 21, 56, 63, 54, 49, 36, 35, 42, 45, 112, 119, 126, 121, 108, 107, 98, 101, 72, 79, 70, 65, 84, 83, 90, 93, 224, 231, 238, 233, 252, 251, 242, 245, 216, 223, 214, 209, 196, 195, 202, 205, 144, 151, 158, 153, 140, 139, 130, 133, 168, 175

Offset: 0

Author

Antti Karttunen, Apr 26 1999

Keywords

• nonn
• easy
• look

Comments

Sequence gives binary encodings of polynomials in maximal ideal generated by x^2 + x + 1 in the polynomial ring GF(2)[X]. E.g. 1 * x^2+x+1 = x^2 +x+1 = 111 (binary encoding) = 7 (in decimal) x * x^2+x+1 = x^3+x^2+x = 1110 = 14 x+1 * x^2+x+1 = x^3+1 = 1001 = 9 x^2 * x^2+x+1 = x^4+x^3+x^2 = 11100 = 28 x^2+1 * x^2+x+1 = x^4+x^3+x+1 = 11011 = 27 etc.

Links

• David A. Corneth, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A048720, A048705, A048710, A048725, A048730.

Programs

Mathematica

A048727[n_] := BitXor[n, 2*n, 4*n];
Array[A048727, 100, 0] (* Paolo Xausa, Aug 06 2025 *)

PARI

a(n)=bitxor(n,bitxor(2*n,4*n)) \\ Charles R Greathouse IV, Oct 03 2016

Python

def A048727(n): return n^ n<<1 ^ n<<2 # Chai Wah Wu, Jun 29 2022