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%I #4 May 03 2017 08:33:12
%S 2,8,17,23,32,41,47,56,62,71,80,86,95,104,110,119,125,134,143,149,158,
%T 164,173,182,188,197,206,212,221,227,236,245,251,260,269,275,284,290,
%U 299,308,314,323,329,338,347,353,362,371,377,386,392,401,410,416,425
%N Positions of 1 in A284394.
%C The sequences p = A032766, q = A285395, r = A284396 of positions of 0,1,2, respectively, partition the positive integers. Let t,u,v be the slopes of p, q, r, respectively. Then t = 3/2, u = (9+3*sqrt(5))/2, v = (3+3*sqrt(5))/2, and 1/t + 1/u + 1/v = 1.
%H Clark Kimberling, <a href="/A284395/b284395.txt">Table of n, a(n) for n = 1..10000</a>
%e As a word, A284394 = 01002001002002001..., in which the positions of 1 are 2,8,17,...
%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] (* A003849 *)
%t w = StringJoin[Map[ToString, s]]; w1 = StringReplace[w, {"101" -> "2"}]
%t st = ToCharacterCode[w1] - 48 (* A284394 *)
%t Flatten[Position[st, 0]] (* A032766 *)
%t Flatten[Position[st, 1]] (* A284395 *)
%t Flatten[Position[st, 2]] (* A284396 *)
%Y Cf. A003849, A032766, A284394, A284396.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 02 2017
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