A349955 Numbers whose representation in any base b >= 2 is a cubefree word.

0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 18, 19, 20, 22, 25, 36, 37, 38, 44, 45, 50, 51, 52, 74, 75, 76, 77, 89, 90, 100, 101, 102, 105, 109, 147, 150, 153, 154, 165, 166, 173, 178, 179, 180, 181, 204, 205, 210, 214, 217, 293, 294, 300, 301, 306, 308, 309, 329, 330

Offset

1,3

Comments

A subsequence of A178905. A subsequence of A286262.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Cubefree Word.

Mathematica

Prepend[Cases[Range[330], n_ /; NoneTrue[Range[2, (Sqrt[4 n - 3] - 1)/2], MatchQ[IntegerDigits[n, #], {___, d__, d__, d__, ___}] &]], 0]

Prog

(Python)
from sympy.ntheory.digits import digits
def hascube(s):
    for l in range(1, len(s)//3 + 1):
      for i in range(len(s) - 3*l + 1):
          if s[i:i+l] == s[i+l:i+2*l] == s[i+2*l:i+3*l]: return True
    return False
def ok(n):
    if n < 7: return True
    b = 2
    d = digits(n, b)[1:]
    while len(d) >= 3:
        if hascube(d):
            return False
        b += 1
        d = digits(n, b)[1:]
    return True
print([k for k in range(331) if ok(k)]) # Michael S. Branicky, Mar 27 2022

Crossrefs

Cf. A178905, A286262.

Sequence in context: A136250 A175585 A178905 * A168009 A134697 A032975

Adjacent sequences: A349952 A349953 A349954 * A349956 A349957 A349958

Keyword

nonn,base

Author

Vladimir Reshetnikov, Mar 20 2022

Status

approved