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%I A081477 #29 Aug 03 2022 23:26:19
%S A081477 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 A081477 43,44,46,48,50,51,53,55,56,58,60,61,63,65,67,68,70,72,73,75,77,79,80,
%U A081477 82,84,85,87,89,90,92,94,96,97,99,101,102,104,106,108,109,111,113,114,116,118
%N A081477 Complement of A086377.
%C A081477 The old entry with this sequence number was a duplicate of A003687.
%C A081477 Is A086377 the sequence of positions of 1 in A189687? - _Clark Kimberling_, Apr 25 2011
%C A081477 The answer to Kimberling's question is: yes. See the Bosma-Dekking-Steiner paper. - _Michel Dekking_, Oct 14 2018
%H A081477 Muniru A Asiru, Table of n, a(n) for n = 1..5000
%H A081477 Wieb Bosma, Michel Dekking, Wolfgang Steiner, A remarkable sequence related to Pi and sqrt(2), arXiv 1710.01498 math.NT (2018).
%H A081477 Wieb Bosma, Michel Dekking, Wolfgang Steiner, A remarkable sequence related to Pi and sqrt(2), Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A4.
%F A081477 Conjectures from _Clark Kimberling_, Aug 03 2022: (Start)
%F A081477 [a(n)*r] = n + [n*r] for n >= 1, where r = sqrt(2) and [ ] = floor.
%F A081477 {a(n)*sqrt(2)} > 1/2 if n is in A120753, where { } = fractional part; otherwise n is in A120752. (End)
%t A081477 t = Nest[Flatten[# /. {0->{0,1,1}, 1->{0,1}}] &, {0}, 5] (*A189687*)
%t A081477 f[n_] := t[[n]]
%t A081477 Flatten[Position[t, 0]] (* A086377 conjectured *)
%t A081477 Flatten[Position[t, 1]] (* A081477 conjectured *)
%t A081477 s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
%t A081477 Table[s[n], {n, 1, 120}] (*A189688*)
%t A081477 (* _Clark Kimberling_, Apr 25 2011 *)
%Y A081477 Cf. A086377, A004641, A189687.
%K A081477 nonn
%O A081477 1,1
%A A081477 _N. J. A. Sloane_, Oct 12 2008
%E A081477 Name corrected by _Michel Dekking_, Jan 04 2019
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