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%I #19 May 24 2019 11:23:29
%S 3,6,7,10,13,14,17,18,21,24,25,28,31,32,35,36,39,42,43,46,47,50,53,54,
%T 57,60,61,64,65,68,71,72,75,78,79,82,83,86,89,90,93,94,97,100,101,104,
%U 107,108,111,112,115,118,119,122,123,126,129,130,133,136,137
%N Positions of 2 in A284749.
%C This sequence and A214971 and A284624 partition the positive integers into sequences with slopes t = (5+sqrt(5))/2, u = (5+sqrt(5))/2, v = sqrt(5), where 1/t + 1/u + 1/v = 1. The positions of 0 in A284749 are given by A214971, and of 1, by A284624.
%H Clark Kimberling, <a href="/A284625/b284625.txt">Table of n, a(n) for n = 1..10000</a>
%H J.-P. Allouche, F. M. Dekking, <a href="https://arxiv.org/abs/1809.03424">Generalized Beatty sequences and complementary triples</a>, arXiv:1809.03424v3 [math.NT], 2018-2019.
%F a(n) = 2*floor(n*phi) - n + 2 (Example 30 in Allouche and Dekking). - _Michel Dekking_, Oct 08 2018
%F a(n) = A050140(n)+2 - _Michel Dekking_, Oct 08 2018
%e As a word, A284749 = 012012201201220122..., in which 2 is in positions 3,6,7,10,...
%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] (* A003849 *)
%t w = StringJoin[Map[ToString, s]]
%t w1 = StringReplace[w, {"001" -> "2"}]
%t st = ToCharacterCode[w1] - 48 (* A284749 *)
%t Flatten[Position[st, 0]] (* A214971 *)
%t Flatten[Position[st, 1]] (* A284624 *)
%t Flatten[Position[st, 2]] (* A284625 *)
%Y Cf. A214971, A284625, A284749.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 02 2017
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