A033002 -id:A033002 - cp's OEIS frontend

A043308 a(n)=A033002(n)/5.

1, 2, 3, 16, 18, 19, 32, 33, 35, 48, 49, 50, 257, 258, 259, 288, 289, 291, 304, 305, 306, 513, 514, 515, 528, 530, 531, 560, 561, 562, 769, 770, 771, 784, 786, 787, 800, 801, 803, 4112, 4114, 4115, 4128, 4129, 4131, 4144, 4145

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 16, have all digits less than 4 and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

Cf. A043307 - A043320, A043291, A033001 - A033014, A033016 - A033029.

is_A043308(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],16))[2]<4 && n[1]%4!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

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

Original entry on oeis.org

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

Clark Kimberling

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

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

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

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

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

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

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

A033017 Numbers whose base-4 expansion has no run of digits with length < 2.

Original entry on oeis.org

5, 10, 15, 21, 42, 63, 80, 85, 90, 95, 160, 165, 170, 175, 240, 245, 250, 255, 320, 336, 341, 346, 351, 362, 383, 640, 661, 672, 677, 682, 687, 703, 960, 981, 1002, 1008, 1013, 1018, 1023, 1280, 1285, 1290, 1295, 1344, 1360, 1365

Offset: 1

Clark Kimberling

Vincenzo Librandi, Table of n, a(n) for n = 1..1600

Cf. A007090. Supersequence of A033002.

Select[Range[1400],Min[Length/@Split[IntegerDigits[#,4]]]>1&] (* Harvey P. Dale, Jun 05 2013 *)

cp's OEIS Frontend

A043308 a(n)=A033002(n)/5.

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

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A033017 Numbers whose base-4 expansion has no run of digits with length < 2.

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