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A193145 Self-composition of binary encoding of GF(2) polynomial. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A302339 A093114 A016740 * A133922 A222954 A240033

Adjacent sequences:  A193142 A193143 A193144 * A193146 A193147 A193148

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Jul 16 2011

STATUS

approved

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Last modified May 16 22:18 EDT 2021. Contains 343957 sequences. (Running on oeis4.)