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

1,1

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A080196 A033025 A044838 * A019551 A098961 A033897

Adjacent sequences: A033007 A033008 A033009 * A033011 A033012 A033013

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved