A081477 - OEIS

A081477

Complement of A086377.

2, 3, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 26, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 102, 104, 106, 108, 109, 111, 113, 114, 116, 118

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

Is A086377 the sequence of positions of 1 in A189687? - Clark Kimberling, Apr 25 2011

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

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Wieb Bosma, Michel Dekking, Wolfgang Steiner, A remarkable sequence related to Pi and sqrt(2), arXiv 1710.01498 math.NT (2018).

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.

FORMULA

Conjectures from Clark Kimberling, Aug 03 2022: (Start)

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

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

MATHEMATICA

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

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

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

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

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

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

(* Clark Kimberling, Apr 25 2011 *)