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A285682 Positions of 1 in A285680.

%I A285682 #12 Mar 11 2025 02:54:58
%S A285682 2,7,14,19,26,33,38,45,50,57,64,69,76,83,88,95,100,107,114,119,126,
%T A285682 131,138,145,150,157,164,169,176,181,188,195,200,207,214,219,226,231,
%U A285682 238,245,250,257,262,269,276,281,288,295,300,307,312,319,326,331,338
%N A285682 Positions of 1 in A285680.
%C A285682 A 3-way partition of the positive integers, by positions of 0, 1, 2 in A285680:
%C A285682 A285681: positions of 0; slope t = (15+sqrt(5))/10;
%C A285682 A285682: positions of 1; slope u = 4+sqrt(5);
%C A285682 A285683: positions of 2; slope v = (1+3*sqrt(5))/2;
%C A285682 where 1/t + 1/u + 1/v = 1. Conjecture: a(n) - a(n-1) is in {5,7} for n >= 2.
%H A285682 Clark Kimberling, <a href="/A285682/b285682.txt">Table of n, a(n) for n = 1..10000</a>
%t A285682 s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] ; (* A003849 *)
%t A285682 w = StringJoin[Map[ToString, s]]
%t A285682 w1 = StringReplace[w, {"1010" -> "2"}]
%t A285682 st = ToCharacterCode[w1] - 48; (* A285680 *)
%t A285682 Flatten[Position[st, 0]];  (* A285681 *)
%t A285682 Flatten[Position[st, 1]];  (* A285682 *)
%t A285682 Flatten[Position[st, 2]];  (* A285683 *)
%Y A285682 Cf. A003849, A285680, A285681, A285683.
%K A285682 nonn,easy
%O A285682 1,1
%A A285682 _Clark Kimberling_, May 11 2017