OFFSET
1,1
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
J.-P. Allouche, F. M. Dekking, Generalized Beatty sequences and complementary triples, arXiv:1809.03424v3 [math.NT], 2018-2019.
FORMULA
a(n) = 3*floor(n*phi) + 2. This follows from Theorem 29 in Allouche and Dekking, since the overlap word 10101 that contains 101 does not occur in the Fibonacci word. Note that v = 3*phi. - Michel Dekking, Oct 17 2018
EXAMPLE
As a word, A284394 = 01002001002002001..., in which the positions of 2 are 5,11,14,...
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] (* A003849 *)
w = StringJoin[Map[ToString, s]]; w1 = StringReplace[w, {"101" -> "2"}]
st = ToCharacterCode[w1] - 48 (* A284394 *)
Flatten[Position[st, 0]] (* A032766, conjectured *)
Flatten[Position[st, 1]] (* A284395 *)
Flatten[Position[st, 2]] (* A284396 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 02 2017
STATUS
approved