cp's OEIS Frontend

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

%I A048727 #29 Aug 08 2025 20:12:40
%S A048727 0,7,14,9,28,27,18,21,56,63,54,49,36,35,42,45,112,119,126,121,108,107,
%T A048727 98,101,72,79,70,65,84,83,90,93,224,231,238,233,252,251,242,245,216,
%U A048727 223,214,209,196,195,202,205,144,151,158,153,140,139,130,133,168,175
%N A048727 a(n) = Xmult(n,7) or rule150(n,1).
%C A048727 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.
%H A048727 David A. Corneth, <a href="/A048727/b048727.txt">Table of n, a(n) for n = 0..8191</a>
%t A048727 A048727[n_] := BitXor[n, 2*n, 4*n];
%t A048727 Array[A048727, 100, 0] (* _Paolo Xausa_, Aug 06 2025 *)
%o A048727 (PARI) a(n)=bitxor(n,bitxor(2*n,4*n)) \\ _Charles R Greathouse IV_, Oct 03 2016
%o A048727 (Python)
%o A048727 def A048727(n): return n^ n<<1 ^ n<<2 # _Chai Wah Wu_, Jun 29 2022
%Y A048727 Cf. A048720, A048705, A048710, A048725, A048730.
%K A048727 nonn,easy,look
%O A048727 0,2
%A A048727 _Antti Karttunen_, Apr 26 1999