A193145 Self-composition of binary encoding of GF(2) polynomial.

0, 1, 2, 2, 16, 16, 18, 19, 512, 584, 674, 749, 912, 973, 770, 856, 65536, 65536, 65538, 65539, 65552, 65553, 65554, 65554, 69120, 69465, 68834, 69052, 68240, 68572, 67650, 67849, 33554432, 34603040, 35652098, 36700721, 37756944, 38805813, 39854162, 40903012, 42084864, 43138625, 44171426, 45225206, 46289296, 47334592, 48396610, 49441799, 52494336

Offset

0,3

Links

Table of n, a(n) for n=0..48.

Example

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.

Prog

(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
a(n) = local(p); p=tox(n); subst(lift(subst(p, X, p)), X, 2)

Crossrefs

Cf. A048720, A000695.

Sequence in context: A093114 A016740 A353915 * A352348 A133922 A222954

Adjacent sequences: A193142 A193143 A193144 * A193146 A193147 A193148

Keyword

nonn

Author

Franklin T. Adams-Watters, Jul 16 2011

Status

approved