OFFSET
1,1
COMMENTS
Indices of c in the sequence closed under a -> abc, b -> a, c -> a, starting with a(1) = a; see A092606 where a = 0, b = 2, c = 1. - Philippe Deléham, Apr 12 2004
These are the positions of 1 in A286044; complement of A286045; conjecture: a(n)/n -> 4. - Clark Kimberling, May 07 2017
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
L. Carlitz, R. Scoville, and V. E. Hoggatt, Jr., Representations for a special sequence, Fibonacci Quarterly 10.5 (1972), 499-518, 550.
FORMULA
Numbers n such that A003159(n) is even. a(n) = A003158(n) + 1 = A036554(n) + n. - Philippe Deléham, Feb 22 2004
EXAMPLE
As a word, A286044 = 001000010010010000100..., in which 1 is in positions a(n) for n>=1. - Clark Kimberling, May 07 2017
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"011" -> "0"}]
st = ToCharacterCode[w1] - 48 (* A286044 *)
Flatten[Position[st, 0]] (* A286045 *)
Flatten[Position[st, 1]] (* A003157 *)
(* Clark Kimberling, May 07 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved