A308009 - OEIS

%I #13 May 15 2019 00:42:48

%S 1,1,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,

%T 0,1,2,0,1,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,

%U 2,0,1,0,1,2,0,1,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2

%N The terms of A081145 appear to lie on three lines; set a(n) = 0 if A081145(n) is on the lower line, 1 if it is on the middle line, and 2 if it is on the upper line.

%C Certainly the first 10^6 terms of A081145 lie on three roughly straight lines, of slopes roughly 0.56, 1.40, 2.24. See the graph of A081145 and the data file of _Allan Wilks_ attached to that entry. It is a strong conjecture that all terms of A081145 lie on three roughly straight lines.

%C In the first 100000 terms, ignoring the initial three terms, usually we see (2,0,1) repeated many times. Occasionally the pattern will be interrupted when (2,0,1) is followed by one or more copies of (0,1) before the repetitions of (2,0,1) resume. The other transitions 0,0; 0,2; 1,1; 2,1; 2,2 seem to never occur.

%C It would be nice to have a better understanding of this sequence.

%H Allan Wilks, <a href="/A308009/b308009.txt">Table of n, a(n) for n = 1..100000</a>

%Y Cf. A081145.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, May 14 2019