A043291 -id:A043291 - cp's OEIS frontend

A033008 Every run of digits of n in base 10 has length 2.

11, 22, 33, 44, 55, 66, 77, 88, 99, 1100, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 2200, 2211, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 3300, 3311, 3322, 3344, 3355, 3366, 3377, 3388, 3399, 4400, 4411, 4422, 4433

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..800

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 10]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

a(n) = 11*A043314(n) (= 11*n for n<10). - M. F. Hasler, Feb 02 2014

A152775 Numbers with 3n binary digits where every run length is 3, written in binary.

Original entry on oeis.org

111, 111000, 111000111, 111000111000, 111000111000111, 111000111000111000, 111000111000111000111, 111000111000111000111000, 111000111000111000111000111, 111000111000111000111000111000

Offset: 1

Omar E. Pol, Jan 18 2009

A152776 written in base 2.

			n ... a(n) .............. A152776(n)
1 ... 111 ............... 7
2 ... 111000 ............ 56
3 ... 111000111 ......... 455
4 ... 111000111000 ...... 3640
5 ... 111000111000111 ... 29127

Vincenzo Librandi, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (1000,1,-1000).

Cf. A043291, A153435, A152776.

FromDigits/@Table[Flatten[PadRight[{},n,{a,b}]/.{a->{1,1,1},b->{0,0,0}}],{n,10}] (* Harvey P. Dale, Mar 23 2012 *)
CoefficientList[Series[111/((x - 1) (x + 1) (1000 x - 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Apr 21 2014 *)

Vec(111*x / ((x-1)*(x+1)*(1000*x-1)) + O(x^100)) \\ Colin Barker, Apr 20 2014

From Colin Barker, Apr 20 2014: (Start)
a(n) = (-1001-999*(-1)^n+2^(4+3*n)*125^(1+n))/18018.
a(n) = 1000*a(n-1)+a(n-2)-1000*a(n-3).
G.f.: 111*x / ((x-1)*(x+1)*(1000*x-1)). (End).

A152776 Numbers such that every run length in base 2 is 3.

Original entry on oeis.org

7, 56, 455, 3640, 29127, 233016, 1864135, 14913080, 119304647, 954437176, 7635497415, 61083979320, 488671834567, 3909374676536, 31274997412295, 250199979298360, 2001599834386887, 16012798675095096, 128102389400760775

Offset: 1

Omar E. Pol, Jan 18 2009

a(n) is the number whose binary representation is A152775(n).

Zak Seidov, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (8, 1, -8).

Cf. A043291, A152775, A153435.

a(n)= 8*a(n-1) +a(n-2) -8*a(n-3). G.f.: 7x/((1-x)(1-8x)(1+x)). a(n)= (-7*(-1)^n-9+16*8^n)/18 = 7*A033118(n). [From R. J. Mathar, Jan 20 2009]

More terms from R. J. Mathar, Jan 20 2009

A033003 Every run of digits of n in base 5 has length 2.

Original entry on oeis.org

6, 12, 18, 24, 150, 162, 168, 174, 300, 306, 318, 324, 450, 456, 462, 474, 600, 606, 612, 618, 3756, 3762, 3768, 3774, 4050, 4056, 4068, 4074, 4200, 4206, 4212, 4224, 4350, 4356, 4362, 4368, 7506, 7512, 7518, 7524, 7650, 7662

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..1000

Select[Range[10000],Union[Length/@Split[IntegerDigits[#, 5]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

a(n) = 6*A043309(n) (= 6*n for n<5). - M. F. Hasler, Feb 02 2014

A033007 Every run of digits of n in base 9 has length 2.

Original entry on oeis.org

10, 20, 30, 40, 50, 60, 70, 80, 810, 830, 840, 850, 860, 870, 880, 890, 1620, 1630, 1650, 1660, 1670, 1680, 1690, 1700, 2430, 2440, 2450, 2470, 2480, 2490, 2500, 2510, 3240, 3250, 3260, 3270, 3290, 3300, 3310, 3320, 4050

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..1000

Select[Range[10000], Union[Length/@Split[IntegerDigits[#, 9]]]=={2}&] (* Vincenzo Librandi, Feb 05 2014 *)

a(n) = 10*A043313(n) (= 10*n for n<9). - M. F. Hasler, Feb 02 2014

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

Original entry on oeis.org

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

A154808 Numbers such that every run length in base 2 is 5.

Original entry on oeis.org

31, 992, 31775, 1016800, 32537631, 1041204192, 33318534175, 1066193093600, 34118178995231, 1091781727847392, 34937015291116575, 1117984489315730400, 35775503658103372831, 1144816117059307930592, 36634115745897853778975

Offset: 1

Omar E. Pol, Jan 25 2009

a(n) is the number whose binary representation is A154807(n).

Harvey P. Dale, Table of n, a(n) for n = 1..664
Index entries for linear recurrences with constant coefficients, signature (32,1,-32).

Cf. A043291, A152776, A154806, A154807.

FromDigits[#,2]&/@Table[PadRight[{},5n,{1,1,1,1,1,0,0,0,0,0}],{n,20}] (* or *) LinearRecurrence[{32,1,-32},{31,992,31775},20] (* Harvey P. Dale, May 08 2016 *)

Conjecture: a(n) = (-33-31*(-1)^n+2^(6+5*n))/66. g.f.: 31*x / ((x-1)*(x+1)*(32*x-1)). - Colin Barker, Sep 16 2013

More terms from Sean A. Irvine, Feb 21 2010

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

cp's OEIS Frontend

A033008 Every run of digits of n in base 10 has length 2.

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A152775 Numbers with 3n binary digits where every run length is 3, written in binary.

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A152776 Numbers such that every run length in base 2 is 3.

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A033003 Every run of digits of n in base 5 has length 2.

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A033007 Every run of digits of n in base 9 has length 2.

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

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A154808 Numbers such that every run length in base 2 is 5.

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

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