A033001 Every run of digits of n in base 3 has length 2.

4, 8, 36, 44, 72, 76, 328, 332, 396, 400, 652, 656, 684, 692, 2952, 2960, 2988, 2992, 3568, 3572, 3600, 3608, 5868, 5876, 5904, 5908, 6160, 6164, 6228, 6232, 26572, 26576, 26640, 26644, 26896, 26900, 26928, 26936, 32112, 32120

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

See A043291 for the base 2 version (which has a very simple formula), A033002 - A033014 for bases 4 through 16, A033015 - A033029 for the variants with runs of length >= 2. - M. F. Hasler, Feb 01 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..250

Programs

Mathematica

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 3]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

PARI

is_A033001(n)=!until(!n\=9,bittest(4588304,n%27)||return)

PARI

for(n=1,9999,is_A033001(n)&&print1(n",")) \\ (End)

PARI

a(n) = my(v=binary(n+1)); v[1]=0; for(i=2,#v, v[i]+=(v[i]>=v[i-1])); 4*fromdigits(v,9); \\ Kevin Ryde, Mar 13 2021

Formula

a(n)=4*A043307(n). - M. F. Hasler, Feb 01 2014