A188383 Positions of 1 in the zero-one sequence [nr+3r]-[nr]-[3r], where r=1/sqrt(2).

7, 14, 24, 31, 41, 48, 55, 65, 72, 82, 89, 96, 106, 113, 123, 130, 140, 147, 154, 164, 171, 181, 188, 195, 205, 212, 222, 229, 239, 246, 253, 263, 270, 280, 287, 294, 304, 311, 321, 328, 335, 345, 352, 362, 369, 379, 386, 393, 403, 410, 420, 427, 434, 444, 451, 461, 468, 478, 485, 492, 502, 509, 519, 526, 533, 543, 550

Offset: 1

Author

Clark Kimberling, Mar 30 2011

Keywords

• nonn

Comments

See A187950.

Positions of 1 in the {0->000, 11->null}-transform of the Sturmian word A080764; see A286996. Also, a(n) - a(n-1) is in {7,10} for n >= 1, and a(n)/n -> 4 + 3*sqrt(2). - Clark Kimberling, May 20 2017

Links

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

Crossrefs

Cf. A187950.

Programs

Mathematica

r=2^(-1/2); k=3;
t=Table[Floor[n*r+k*r]-Floor[n*r]-Floor[k*r], {n,1,220}]
Flatten[Position[t,1] ] (* A188383 *)

Python

from _future_ import division
from gmpy2 import isqrt
A188383_list = [n for n in range(1,10**6) if isqrt((n+3)**2//2) - isqrt(n**2//2) == 3] # Chai Wah Wu, Oct 08 2016