A033014 Every run of digits of n in base 16 has length 2.

17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 4352, 4386, 4403, 4420, 4437, 4454, 4471, 4488, 4505, 4522, 4539, 4556, 4573, 4590, 4607, 8704, 8721, 8755, 8772, 8789, 8806, 8823, 8840, 8857, 8874

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Examples

			In base 16, a(1)=17 is written 11; the subsequent 14 values are the multiples of 17, corresponding to 22, 33, 44, ..., FF.
This is followed by a(16) = 4352 = 1100[16], then (still in base 16): 1122, 1133,..., 11FF, 2200, 2211, 2233, etc...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Crossrefs

See A033001 for further cross-references.

Programs

Mathematica

Select[Range[9000],Union[Length/@Split[IntegerDigits[#,16]]]=={2}&] (* Harvey P. Dale, Jan 19 2013 *)

Python

from itertools import count, islice, groupby
def A033014_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:set(len(list(g)) for k, g in groupby(hex(n)[2:]))=={2},count(max(startvalue,1)))
A033014_list = list(islice(A033014_gen(),20)) # Chai Wah Wu, Mar 10 2023

Formula

a(n) = 17*A043320(n) (= 17n for n<16, cf Example). - M. F. Hasler, Feb 02 2014