This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A284396 #21 May 24 2019 11:23:12
%S A284396 5,11,14,20,26,29,35,38,44,50,53,59,65,68,74,77,83,89,92,98,101,107,
%T A284396 113,116,122,128,131,137,140,146,152,155,161,167,170,176,179,185,191,
%U A284396 194,200,203,209,215,218,224,230,233,239,242,248,254,257,263,266,272
%N A284396 Positions of 2 in A284394.
%C A284396 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 A284396 Clark Kimberling, <a href="/A284396/b284396.txt">Table of n, a(n) for n = 1..10000</a>
%H A284396 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 A284396 a(n) = 3*floor(n*phi) + 2. This follows from Theorem 29 in Allouche and Dekking, since the overlap word 10101 that contains 101 does not occur in the Fibonacci word. Note that v = 3*phi. - _Michel Dekking_, Oct 17 2018
%e A284396 As a word, A284394 = 01002001002002001..., in which the positions of 2 are 5,11,14,...
%t A284396 s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] (* A003849 *)
%t A284396 w = StringJoin[Map[ToString, s]]; w1 = StringReplace[w, {"101" -> "2"}]
%t A284396 st = ToCharacterCode[w1] - 48 (* A284394 *)
%t A284396 Flatten[Position[st, 0]] (* A032766, conjectured *)
%t A284396 Flatten[Position[st, 1]] (* A284395 *)
%t A284396 Flatten[Position[st, 2]] (* A284396 *)
%Y A284396 Cf. A003849, A032766, A284394, A284395.
%K A284396 nonn,easy
%O A284396 1,1
%A A284396 _Clark Kimberling_, May 02 2017