A191153 - OEIS

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A191153

a(n) = floor(2*n*Pi) - 2*floor(n*Pi).

0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1

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

OFFSET

COMMENTS

Equivalently, the nearest integer to the fractional part of n*Pi. - Rick L. Shepherd, Aug 24 2020

Up to n = 53 (respectively n = 16551), the sequence appears to be 7-periodic (a(n) = a(n-7); 000 1111 repeated), respectively 113-periodic. This is a consequence of the fact that 7*Pi and 113*Pi are close to an integer: Pi ~ 355/113 ~ 22/7. - M. F. Hasler, Nov 30 2024

LINKS

Rick L. Shepherd, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A038130(n) - 2*A022844(n). - Michel Marcus, Aug 24 2020

MAPLE

A191153:=n->floor(2*n*Pi) - 2*floor(n*Pi): seq(A191153(n), n=1..100); # Wesley Ivan Hurt, Jul 03 2014

MATHEMATICA

f[n_] := Floor[2 n*Pi] - 2*Floor[n*Pi];

t = Table[f[n], {n, 1, 220}] (* A191153 *)

Flatten[Position[t, 0]] (* A191159 *)

Flatten[Position[t, 1]] (* A191164 *)

PROG