A286938 - OEIS

%I #4 Jun 04 2017 18:18:14

%S 2,3,5,8,13,21,33,52,82,128,200,313,488,761,1188,1852,2887,4503,7020,

%T 10943,17063,26601,41468,64652,100792,157128,244965,381898,595363,

%U 928166,1446998,2255827,3516797,5482628,8547285,13325053,20773513,32385456

%N Length of n-th iterate of the mapping 00->001, 1->10, as in A284932.

%C Appears to be identical to A164457 except for the initial terms 2,3,5.

%F Conjecture:  a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) -3*a(n-4) + a(n-5) for 5 >= 0.

%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

%t w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "10"}]

%t Table[w[n], {n, 0, 8}]

%t st = ToCharacterCode[w[11]] - 48   (* A284932 *)

%t Flatten[Position[st, 0]]  (* A285352 *)

%t Flatten[Position[st, 1]]  (* A285303 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A286938 *)

%Y Cf. A284932, A164457.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Jun 03 2017