OFFSET
1,1
COMMENTS
A 3-way partition of the positive integers, by positions of 0, 1, 2 in A285677:
A285678: positions of 0; slope t = (4+sqrt(5))/2;
A182761: positions of 1; slope u = (7-sqrt(5))/2;
A285679: positions of 2; slope v = (1+3*sqrt(5))/2;
where 1/t + 1/u + 1/v = 1.
Conjecture: a(n) - a(n-1) is in {2,5} for n>=2.
See A285683 for a proof of this conjecture. - Michel Dekking, Oct 09 2018
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 3*floor((n-1)*phi) - n + 4
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0010" -> "2"}]
st = ToCharacterCode[w1] - 48; (* A285677 *)
Flatten[Position[st, 0]]; (* A285678 *)
Flatten[Position[st, 1]]; (* A182761 *)
Flatten[Position[st, 2]]; (* A285679 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 11 2017
STATUS
approved