A308009 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.

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, 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, 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

Offset

1,4

Comments

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.

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.

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

Links

Allan Wilks, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A081145.

Sequence in context: A134979 A112248 A244860 * A010872 A220663 A220659

Adjacent sequences: A308006 A308007 A308008 * A308010 A308011 A308012

Keyword

nonn

Author

N. J. A. Sloane, May 14 2019

Status

approved