A178905 Numbers without 3 consecutive equal digits in any base b >= 2.

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, 212, 214, 217, 293, 294, 299, 300, 301, 306, 308, 309, 329

Offset: 1

Author

Joonas Pohjonen, Jun 22 2010

Keywords

• base
• nonn

Links

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

Crossrefs

Cf. A063037.

Programs

Mathematica

Prepend[Cases[Range[329], n_ /; NoneTrue[Range[2, (Sqrt[4 n - 3] - 1)/2], MatchQ[IntegerDigits[n, #], {_, d_, d_, d_, _}] &]], 0] (* Vladimir Reshetnikov, Mar 20 2022 *)

Python

from sympy.ntheory.digits import digits
def three_in_a_row(s):
    return any(s[i] == s[i+1] == s[i+2] for i in range(len(s) - 2))
def ok(n):
    if n < 7: return True
    b = 2
    d = digits(n, b)[1:]
    while len(d) >= 3:
        if three_in_a_row(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