A214215 - OEIS

%I #12 Nov 22 2020 12:22:32

%S 1,2,11,12,21,22,112,121,122,211,212,221,1121,1122,1211,1212,1221,

%T 2112,2121,2122,2211,2212,11212,11221,12112,12122,12211,12212,21121,

%U 21122,21211,21221,22112,22121,112122,112211,112212,121121,121122,121221,122112,122121

%N List of subwords (or factors) of the Thue-Morse "1,2"-word A001285.

%C The number of factors of length m is given by A005942(m).

%H Alois P. Heinz, <a href="/A214215/b214215.txt">Table of n, a(n) for n = 1..10200</a>

%p b:= proc(n) option remember; local r;

%p       `if`(n=0, 1, `if`(n<4, 2*n, `if`(irem(n, 2, 'r')=0,

%p        b(r)+b(r+1), 2*b(r+1))))

%p     end:

%p m:= proc(n) option remember; local r;

%p       `if`(n=0, 1, `if`(irem(n, 2, 'r')=0, m(r), 3-m(r)))

%p     end:

%p T:= proc(n) local k, s; s:={};

%p       for k while nops(s)<b(n) do

%p         s:= s union {parse(cat(seq(m(i), i=k..k+n-1)))}

%p       od; sort([s[]])[]

%p     end:

%p seq(T(n), n=1..10);  # _Alois P. Heinz_, Jul 19 2012

%t b[n_] := b[n] = Module[{r}, If[n == 0, 1, If[n < 4, 2n, r = Quotient[n, 2]; If[Mod[n, 2] == 0, b[r] + b[r + 1], 2b[r + 1]]]]];

%t m[n_] := m[n] = Module[{r}, If[n == 0, 1, r = Quotient[n, 2]; If[Mod[n, 2] == 0, m[r], 3 - m[r]]]];

%t T[n_] := Module[{k, s = {}}, For[k = 1,  Length[s] < b[n], k++, s = s  ~Union~ {FromDigits[#]}& @ Table[m[i], {i, k, k + n - 1}]]; Sort[s]];

%t Array[T, 10] // Flatten (* _Jean-François Alcover_, Nov 22 2020, after _Alois P. Heinz_ *)

%Y Cf. A001285, A010060, A005942.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jul 10 2012