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%I #4 May 11 2017 20:10:28
%S 1,6,8,13,15,18,20,25,27,32,34,37,39,44,46,49,51,56,58,63,65,68,70,75,
%T 77,82,84,87,89,94,96,99,101,106,108,113,115,118,120,125,127,130,132,
%U 137,139,144,146,149,151,156,158,163,165,168,170,175,177,180,182
%N Positions of 0 in A285677.
%C A 3-way partition of the positive integers, by positions of 0, 1, 2 in A285677:
%C A285678: positions of 0; slope t = (4+sqrt(5))/2;
%C A182761: positions of 1; slope u = (7-sqrt(5))/2;
%C A285679: positions of 2; slope v = (1+3*sqrt(5))/2;
%C where 1/t + 1/u + 1/v = 1. Conjecture: a(n) - a(n-1) is in {2,3,4,5} for n>=2.
%H Clark Kimberling, <a href="/A285678/b285678.txt">Table of n, a(n) for n = 1..10000</a>
%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)
%t w = StringJoin[Map[ToString, s]]
%t w1 = StringReplace[w, {"0010" -> "2"}]
%t st = ToCharacterCode[w1] - 48; (* A285677 *)
%t Flatten[Position[st, 0]]; (* A285678 *)
%t Flatten[Position[st, 1]]; (* A182761 *)
%t Flatten[Position[st, 2]]; (* A285679 *)
%Y Cf. A003849, A284620, A285678, A182761, A285679.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, May 11 2017
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