Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Mar 30 2012 17:35:24
%S 0,1,2,2,16,16,18,19,512,584,674,749,912,973,770,856,65536,65536,
%T 65538,65539,65552,65553,65554,65554,69120,69465,68834,69052,68240,
%U 68572,67650,67849,33554432,34603040,35652098,36700721,37756944,38805813,39854162,40903012,42084864,43138625,44171426,45225206,46289296,47334592,48396610,49441799,52494336
%N Self-composition of binary encoding of GF(2) polynomial.
%e 7, 111 in base 2, is transformed to the polynomial x^2+x+1. Composing this with itself (mod 2) gives (x^2+x+1)^2 + (x^2+x+1) + 1 = x^4+x+1, which transforms back to 19; so a(7) = 19.
%o (PARI) tox(n) = local(x=Mod(1,2)*X, xp=1, r); while(n>0,if(n%2,r+=xp);xp*=x;n\=2);r
%o a(n) = local(p); p=tox(n);subst(lift(subst(p,X,p)),X,2)
%Y Cf. A048720, A000695.
%K nonn
%O 0,3
%A _Franklin T. Adams-Watters_, Jul 16 2011