%I #29 Aug 03 2022 23:26:19

%S 2,3,5,7,9,10,12,14,15,17,19,20,22,24,26,27,29,31,32,34,36,38,39,41,

%T 43,44,46,48,50,51,53,55,56,58,60,61,63,65,67,68,70,72,73,75,77,79,80,

%U 82,84,85,87,89,90,92,94,96,97,99,101,102,104,106,108,109,111,113,114,116,118

%N Complement of A086377.

%C The old entry with this sequence number was a duplicate of A003687.

%C Is A086377 the sequence of positions of 1 in A189687? - _Clark Kimberling_, Apr 25 2011

%C The answer to Kimberling's question is: yes. See the Bosma-Dekking-Steiner paper. - _Michel Dekking_, Oct 14 2018

%H Muniru A Asiru, <a href="/A081477/b081477.txt">Table of n, a(n) for n = 1..5000</a>

%H Wieb Bosma, Michel Dekking, Wolfgang Steiner, <a href="https://arxiv.org/abs/1710.01498">A remarkable sequence related to Pi and sqrt(2)</a>, arXiv 1710.01498 math.NT (2018).

%H Wieb Bosma, Michel Dekking, Wolfgang Steiner, <a href="http://math.colgate.edu/~integers/sjs4/sjs4.Abstract.html">A remarkable sequence related to Pi and sqrt(2)</a>, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A4.

%F Conjectures from _Clark Kimberling_, Aug 03 2022: (Start)

%F [a(n)*r] = n + [n*r] for n >= 1, where r = sqrt(2) and [ ] = floor.

%F {a(n)*sqrt(2)} > 1/2 if n is in A120753, where { } = fractional part; otherwise n is in A120752. (End)

%t t = Nest[Flatten[# /. {0->{0,1,1}, 1->{0,1}}] &, {0}, 5] (*A189687*)

%t f[n_] := t[[n]]

%t Flatten[Position[t, 0]] (* A086377 conjectured *)

%t Flatten[Position[t, 1]] (* A081477 conjectured *)

%t s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;

%t Table[s[n], {n, 1, 120}] (*A189688*)

%t (* _Clark Kimberling_, Apr 25 2011 *)

%Y Cf. A086377, A004641, A189687.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Oct 12 2008

%E Name corrected by _Michel Dekking_, Jan 04 2019