A043291 -id:A043291 - cp's OEIS frontend

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

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

A043317 a(n)=A033011(n)/14.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 169, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 338, 339, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 507, 508, 509, 511, 512, 513, 514, 515, 516, 517, 518, 519, 676, 677, 678

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 169, have all digits less than 13 and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Select[Range[700],Max[IntegerDigits[#,169]]<13&&SequenceCount[ IntegerDigits[ #,169],{x_,x_}]==0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 07 2018 *)

is_A043317(n)=(n=[n])&&!until(!n[1],((n=divrem(n,169))[2]<13 && n[2]!=n[1]%13)||return) \\ M. F. Hasler, Feb 03 2014

A043319 a(n)=A033013(n)/16.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 225, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 450, 451, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 675, 676, 677, 679, 680, 681, 682, 683, 684

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 225, have all digits less than 15 and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

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

is_A043319(n)=(n=[n])&&!until(!n[1], ((n=divrem(n[1], 225))[2]<15 && n[1]%15!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

A154806 Numbers such that every run length in base 2 is 4.

Original entry on oeis.org

15, 240, 3855, 61680, 986895, 15790320, 252645135, 4042322160, 64677154575, 1034834473200, 16557351571215, 264917625139440, 4238682002231055, 67818912035696880, 1085102592571150095, 17361641481138401520

Offset: 1

Omar E. Pol, Jan 25 2009

a(n) is the number whose binary representation is A154805(n).

Index entries for linear recurrences with constant coefficients, signature (16,1,-16).

Cf. A043291, A097262, A152776, A154805, A154808.

LinearRecurrence[{16,1,-16},{15,240,3855},20] (* Harvey P. Dale, Apr 13 2018 *)

Conjecture: a(n) = 1/17*2^(4*n+4) + 15/34*(-1)^(n+1) - 1/2. - Vaclav Kotesovec, Nov 30 2012

Empirical g.f.: 15*x / ((x-1)*(x+1)*(16*x-1)). - Colin Barker, Sep 16 2013

More terms from Sean A. Irvine, Feb 21 2010

A249907 Smallest positive integer k such that k contains all possible pairs of digits when represented in base b = n >= 2.

Original entry on oeis.org

19, 20842, 4387884733, 301083852338952371, 10372871309299412994565980691, 257810894191937039020949293796466032151538, 6291283822228991408060146690794416231996294644948906012153, 196933489270977741064964174271054692081510750312035993579769632880958095885917

Offset: 2

Anthony Sand, Nov 08 2014

In base b, there are b^2 distinct pairs of digits and the smallest positive integer to contain all of them will have (b^2)+1 digits. For example, in base 2 there are 2^2 = 4 distinct pairs: 00, 01, 10, 11. All of them are represented in the 5-digit binary number 10011 = 19 in base 10.

			n = 2: a(2) = 19 = 10011 in base 2, which contains 4 distinct pairs of digits: 10, 00, 01, 11.
n = 3: a(3) = 20842 = 1001120221 in base 3, which contains 9 distinct pairs of digits: 10, 00, 01, 11, 12, 20, 22, 21.
n = 4: a(4) = 4387884733 = 10011202130322331 in base 4, which contains 16 distinct pairs of digits: 10, 00, 01, 11, 12, 20, 02, 21, 13, 30, 03, 32, 22, 23, 33, 31.
In base 10, all pairs from 00 to 99 are found in the 101 digits of [1, 0, 0, 1, 1, 2, 0, 2, 1, 3, 0, 3, 1, 4, 0, 4, 1, 5, 0, 5, 1, 6, 0, 6, 1, 7, 0, 7, 1, 8, 0, 8, 1, 9, 0, 9, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 5, 5, 6, 5, 7,5, 8, 5, 9, 6, 6, 7, 6, 8, 6, 9, 7, 7, 8, 7, 9, 8, 8, 9, 9, 1].

Anthony Sand, Table of n, a(n) for n = 2..40

Cf. A033008, A043291.

Edited: minor changes in the name, comment and example. - Wolfdieter Lang, Nov 21 2014

cp's OEIS Frontend

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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Mathematica

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

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PARI

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

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Maple

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A043317 a(n)=A033011(n)/14.

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Mathematica

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A043319 a(n)=A033013(n)/16.

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A154806 Numbers such that every run length in base 2 is 4.

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