A188374 [nr+kr]-[nr]-[kr], where r=1/sqrt(2), k=2, [ ]=floor.

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

Offset

1

Comments

See A187950. For k=1 instead of 2, see A080764 for which the position sequences of 0 and 1 are A001952 and A001951, respectively.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n)=[nr+2r]-[nr]-[2r], where r=1/sqrt(2).

Mathematica

r=2^(-1/2); k=2;
t=Table[Floor[n*r+k*r]-Floor[n*r]-Floor[k*r], {n, 1, 220}]   (* A188374 *)
Flatten[Position[t, 0] ]   (* A188375 *)
Flatten[Position[t, 1] ]   (* A188376 *)

Prog

(Python)
from __future__ import division
from gmpy2 import isqrt
def A188374(n):
    return int(isqrt((n+2)**2//2)-isqrt(n**2//2)) - 1 # Chai Wah Wu, Oct 08 2016

Crossrefs

Cf. A187950, A188375, A188376, A080764.

Sequence in context: A289034 A011747 A089013 * A123504 A273511 A104015

Adjacent sequences: A188371 A188372 A188373 * A188375 A188376 A188377

Keyword

nonn

Author

Clark Kimberling, Mar 29 2011

Status

approved