OFFSET
1,1
COMMENTS
Cubefree means that there is no substring which is the repetition of three identical nonempty strings, see examples.
If n is in the sequence, any number of the form n*2^k + m with 0 <= m < 2^k is in the sequence, and also any number of the form m*2^k + n with 2^k > n, m >= 0.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ n: the sequence has asymptotic density one.
EXAMPLE
7 is in the sequence, because 7 = 111[2] contains three consecutive "1"s.
8 is in the sequence, because 8 = 1000[2] contains three consecutive "0"s.
42 is in the sequence, because 42 = 101010[2] contains three consecutive "10"s.
From the comment follows that all numbers of the form 7*2^k, 8*2^k or 42*2^k are in the sequence, for any k >= 0.
All numbers congruent to 7 or congruent to 0 (mod 8) are in the sequence.
All numbers of the form m*2^(k+3) +- n with n < 2^k are in the sequence.
PROG
(Python)
from __future__ import division
def is_cubefree(s):
l = len(s)
for i in range(l-2):
for j in range(1, (l-i)//3+1):
if s[i:i+2*j] == s[i+j:i+3*j]:
return False
return True
A286261_list = [n for n in range(10**4) if not is_cubefree(bin(n)[2:])] # Chai Wah Wu, May 06 2017
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, May 05 2017
STATUS
approved