A289013 - OEIS

A289013

Positions of 1 in A289011; complement of A289012.

3, 5, 8, 13, 16, 20, 22, 27, 30, 34, 37, 40, 44, 46, 51, 54, 58, 61, 63, 68, 71, 75, 78, 81, 85, 87, 92, 95, 99, 102, 104, 107, 112, 116, 119, 121, 126, 128, 133, 136, 138, 143, 145, 148, 153, 157, 160, 162, 167, 169, 174, 177, 180, 182, 187, 191, 194, 198

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OFFSET

1,1

COMMENTS

Conjecture: a(n)/n -> 2 + sqrt(2), and 0 < 2 + sqrt(2) - a(n)/n < 1 for n >= 1.

LINKS

Table of n, a(n) for n=1..58.

MATHEMATICA

z = 11; (* number of iterates *)

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

w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "100"}]

TableForm[Table[w[n], {n, 0, 10}]]