A033010 Numbers each of whose runs of digits in base 12 has length 2.

13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 1872, 1898, 1911, 1924, 1937, 1950, 1963, 1976, 1989, 2002, 2015, 3744, 3757, 3783, 3796, 3809, 3822, 3835, 3848, 3861, 3874, 3887, 5616, 5629, 5642, 5668, 5681, 5694, 5707, 5720, 5733, 5746, 5759, 7488, 7501

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

See A043291 and A033001 through A033014 for the analog in other bases, A033015 - A033029 for the variants with run lengths >= 2. - M. F. Hasler, Feb 02 2014

Numbers without repeating adjacent digits for which all digits are divisible by 13, in base 144. Consequently there are 11^n n-digit members of this sequence (base 144) and so (11^(n+1)-1)/10 members of this sequence below 144^n. - Charles R Greathouse IV, Feb 02 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1400

Programs

Mathematica

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 12]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

Python

from sympy.ntheory import digits
from itertools import groupby
def ok(n):
  return all(len(list(g))==2 for k, g in groupby(digits(n, 12)[1:]))
print(list(filter(ok, range(1, 7502)))) # Michael S. Branicky, Apr 27 2021

Formula

a(n) = 13*A043316(n) (= 13*n for n < 12). - M. F. Hasler, Feb 02 2014