|
|
|
|
3, 5, 8, 12, 14, 18, 21, 23, 26, 30, 33, 35, 39, 41, 44, 48, 50, 54, 57, 59, 63, 65, 68, 72, 75, 77, 80, 84, 86, 90, 93, 95, 98, 102, 105, 107, 111, 113, 116, 120, 123, 125, 128, 132, 134, 138, 141, 143, 147, 149, 152, 156, 158, 162, 165, 167, 170, 174, 177
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Conjecture: 3n - a(n) is in {0, 1} for n >= 1.
Proof of the conjecture: Let t = A010060 be the Thue-Morse sequence. Every pair t(2n-1),t(2n) is either 01 or 10. Since 01 and 10 map to 110 and 101 under the transform, which both have length 3, it follows that a(n) = 3n-1+t(2n) for n=1,2,..., and so certainly 3n - a(n) is 0 or 1. - Michel Dekking, Jan 05 2018
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
As a word, A285952 = 110101101110101..., in which 0 is in positions 3,5,8,12,...
|
|
MATHEMATICA
|
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 7] (* Thue-Morse, A010060 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" -> "1", "1" -> "10"}] (* A285952, word *)
st = ToCharacterCode[w1] - 48 (* A285952, sequence *)
Flatten[Position[st, 0]] (* A285953 *)
Flatten[Position[st, 1]] (* A285954 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|