A033001 -id:A033001 - cp's OEIS frontend

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

Clark Kimberling

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

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

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

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

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

A033004 Every run of digits of n in base 6 has length 2.

Original entry on oeis.org

7, 14, 21, 28, 35, 252, 266, 273, 280, 287, 504, 511, 525, 532, 539, 756, 763, 770, 784, 791, 1008, 1015, 1022, 1029, 1043, 1260, 1267, 1274, 1281, 1288, 9079, 9086, 9093, 9100, 9107, 9576, 9583, 9597, 9604, 9611, 9828, 9835

Offset: 1

Clark Kimberling

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

Vincenzo Librandi, Table of n, a(n) for n = 1..700

Cf. A033007, A033010.

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 6]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

a(n) = 7*A043310(n) (= 7*n for n<6). - M. F. Hasler, Feb 02 2014

A033005 Every run of digits of n in base 7 has length 2.

Original entry on oeis.org

8, 16, 24, 32, 40, 48, 392, 408, 416, 424, 432, 440, 784, 792, 808, 816, 824, 832, 1176, 1184, 1192, 1208, 1216, 1224, 1568, 1576, 1584, 1592, 1608, 1616, 1960, 1968, 1976, 1984, 1992, 2008, 2352, 2360, 2368, 2376, 2384, 2392

Offset: 1

Clark Kimberling

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1500

Select[Range[2500],Union[Length/@Split[IntegerDigits[#,7]]]=={2}&] (* Harvey P. Dale, Oct 24 2011 *)

a(n) = 8*A043311(n) (= 8*n for n<7). - M. F. Hasler, Feb 02 2014

A033006 Every run of digits of n in base 8 has length 2.

Original entry on oeis.org

9, 18, 27, 36, 45, 54, 63, 576, 594, 603, 612, 621, 630, 639, 1152, 1161, 1179, 1188, 1197, 1206, 1215, 1728, 1737, 1746, 1764, 1773, 1782, 1791, 2304, 2313, 2322, 2331, 2349, 2358, 2367, 2880, 2889, 2898, 2907, 2916, 2934

Offset: 1

Clark Kimberling

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

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

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 8]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

a(n) = 9*A043312(n) (= 9*n for n<8). - M. F. Hasler, Feb 02 2014

Typo in name corrected by Vincenzo Librandi, Feb 05 2014

A033009 Every run of digits of n in base 11 has length 2.

Original entry on oeis.org

12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 1452, 1476, 1488, 1500, 1512, 1524, 1536, 1548, 1560, 1572, 2904, 2916, 2940, 2952, 2964, 2976, 2988, 3000, 3012, 3024, 4356, 4368, 4380, 4404, 4416, 4428, 4440, 4452, 4464, 4476

Offset: 1

Clark Kimberling

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1100

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 11]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

a(n) = 12*A043315(n) (= 12*n for n<11). - M. F. Hasler, Feb 02 2014

A033011 Every run of digits of n in base 13 has length 2.

Original entry on oeis.org

14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 2366, 2394, 2408, 2422, 2436, 2450, 2464, 2478, 2492, 2506, 2520, 2534, 4732, 4746, 4774, 4788, 4802, 4816, 4830, 4844, 4858, 4872, 4886, 4900, 7098, 7112, 7126, 7154

Offset: 1

Clark Kimberling

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1800

Select[Range[8000],Union[Length/@Split[IntegerDigits[#,13]]]=={2}&] (* Harvey P. Dale, Feb 27 2013 *)

a(n) = 14*A043317(n) (= 14*n for n<13). - M. F. Hasler, Feb 02 2014

A033012 Every run of digits of n in base 14 has length 2.

Original entry on oeis.org

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 2940, 2970, 2985, 3000, 3015, 3030, 3045, 3060, 3075, 3090, 3105, 3120, 3135, 5880, 5895, 5925, 5940, 5955, 5970, 5985, 6000, 6015, 6030, 6045, 6060, 6075, 8820

Offset: 1

Clark Kimberling

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 04 2014

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

Select[Range[9000],Union[Length/@Split[IntegerDigits[#,14]]]=={2}&] (* Harvey P. Dale, Apr 26 2013 *)

a(n) = 15*A043318(n) (= 15*n for n<14). - M. F. Hasler, Feb 02 2014

A033013 Every run of digits of n in base 15 has length 2.

Original entry on oeis.org

16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 3600, 3632, 3648, 3664, 3680, 3696, 3712, 3728, 3744, 3760, 3776, 3792, 3808, 3824, 7200, 7216, 7248, 7264, 7280, 7296, 7312, 7328, 7344, 7360, 7376, 7392

Offset: 1

Clark Kimberling

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 04 2014

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

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 15]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

a(n) = 16*A043319(n) (= 16n for n<15). - M. F. Hasler, Feb 02 2014

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

Original entry on oeis.org

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

A043312 a(n) = A033006(n)/9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 64, 66, 67, 68, 69, 70, 71, 128, 129, 131, 132, 133, 134, 135, 192, 193, 194, 196, 197, 198, 199, 256, 257, 258, 259, 261, 262, 263, 320, 321, 322, 323, 324, 326, 327, 384, 385, 386, 387, 388, 389, 391, 448, 449

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 64, have only digits 0 through 7, and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

Robert Israel, Table of n, a(n) for n = 1..10000

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

f:= proc(n) local i;
      seq(64*n+i, i= subs(n mod 64 = NULL, [$0..7]))
end proc:
A:= $1..7: R:= [A]:
for d from 2 to 3 do
  R:= map(f, R);
  A:= A, op(R);
od:
A; # Robert Israel, Jun 11 2019

is_A043312(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],64))[2]<8 && n[1]%8!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

cp's OEIS Frontend

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

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A033004 Every run of digits of n in base 6 has length 2.

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A033005 Every run of digits of n in base 7 has length 2.

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A033006 Every run of digits of n in base 8 has length 2.

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A033009 Every run of digits of n in base 11 has length 2.

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A033011 Every run of digits of n in base 13 has length 2.

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A033012 Every run of digits of n in base 14 has length 2.

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A033013 Every run of digits of n in base 15 has length 2.

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

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