# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a081477 Showing 1-1 of 1 %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE