A043320 -id:A043320 - cp's OEIS frontend

A033014 Every run of digits of n in base 16 has length 2.

17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 4352, 4386, 4403, 4420, 4437, 4454, 4471, 4488, 4505, 4522, 4539, 4556, 4573, 4590, 4607, 8704, 8721, 8755, 8772, 8789, 8806, 8823, 8840, 8857, 8874

Offset: 1

Clark Kimberling

			In base 16, a(1)=17 is written 11; the subsequent 14 values are the multiples of 17, corresponding to 22, 33, 44, ..., FF.
This is followed by a(16) = 4352 = 1100[16], then (still in base 16): 1122, 1133,..., 11FF, 2200, 2211, 2233, etc...

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

See A033001 for further cross-references.

Select[Range[9000],Union[Length/@Split[IntegerDigits[#,16]]]=={2}&] (* Harvey P. Dale, Jan 19 2013 *)

from itertools import count, islice, groupby
def A033014_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:set(len(list(g)) for k, g in groupby(hex(n)[2:]))=={2},count(max(startvalue,1)))
A033014_list = list(islice(A033014_gen(),20)) # Chai Wah Wu, Mar 10 2023

a(n) = 17*A043320(n) (= 17n for n<16, cf Example). - M. F. Hasler, Feb 02 2014

A043307 a(n) = A033001(n)/4.

Original entry on oeis.org

1, 2, 9, 11, 18, 19, 82, 83, 99, 100, 163, 164, 171, 173, 738, 740, 747, 748, 892, 893, 900, 902, 1467, 1469, 1476, 1477, 1540, 1541, 1557, 1558, 6643, 6644, 6660, 6661, 6724, 6725, 6732, 6734, 8028, 8030, 8037, 8038, 8101, 8102, 8118, 8119

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 9, have only digits 0, 1 or 2, and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

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

Cf. A043308 - A043320, A043291, A033001 - A033014, A033016 - A033029.

A[1]:= [1,2]:
for d from 2 to 6 do
  A[d]:= map(t -> seq(9*t+j,j=subs(t mod 9 = NULL, [0,1,2])), A[d-1])
od:
seq(op(A[d]),d=1..6); # Robert Israel, Jan 29 2017

Table[FromDigits[#,9]&/@Select[Tuples[{0,1,2},n],Min[Abs[Differences[#]]]>0&],{n,2,5}]// Flatten// Union (* Harvey P. Dale, May 27 2023 *)

is_A043307(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],9))[2]<3 && n[1]%3!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

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

From Robert Israel, Jan 29 2017: (Start)
If a(n) == 0 (mod 3) then a(2*n+1) = 9*a(n) + 1 else a(2*n+1) = 9*a(n).
If a(n) == 2 (mod 3) then a(2*n+2) = 9*a(n) + 1 else a(2*n+1) = 9*a(n)+2.
a(4k+5) = 9*a(2k+2).
(End)

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

A043309 a(n)=A033003(n)/6.

Original entry on oeis.org

1, 2, 3, 4, 25, 27, 28, 29, 50, 51, 53, 54, 75, 76, 77, 79, 100, 101, 102, 103, 626, 627, 628, 629, 675, 676, 678, 679, 700, 701, 702, 704, 725, 726, 727, 728, 1251, 1252, 1253, 1254, 1275, 1277, 1278, 1279, 1325, 1326, 1327, 1329

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 25, have all digits less than 5 and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

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

is_A043309(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],25))[2]<5 && n[1]%5!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

A043310 a(n)=A033004(n)/7.

Original entry on oeis.org

1, 2, 3, 4, 5, 36, 38, 39, 40, 41, 72, 73, 75, 76, 77, 108, 109, 110, 112, 113, 144, 145, 146, 147, 149, 180, 181, 182, 183, 184, 1297, 1298, 1299, 1300, 1301, 1368, 1369, 1371, 1372, 1373, 1404, 1405, 1406, 1408, 1409, 1440, 1441, 1442, 1443, 1445, 1476, 1477

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 36, have all digits less than 6 and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

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

is_A043310(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],36))[2]<6 && n[1]%6!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

Definition corrected by and more terms from Georg Fischer, Mar 04 2021

A043311 a(n)=A033005(n)/8.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 49, 51, 52, 53, 54, 55, 98, 99, 101, 102, 103, 104, 147, 148, 149, 151, 152, 153, 196, 197, 198, 199, 201, 202, 245, 246, 247, 248, 249, 251, 294, 295, 296, 297, 298, 299, 2402, 2403, 2404, 2405, 2406, 2407, 2499

Offset: 1

Clark Kimberling

Numbers which, written in base 49, have only digits 0 through 6 and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

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

is_A043311(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],49))[2]<7 && n[1]%7!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

A043313 a(n)=A033007(n)/10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 81, 83, 84, 85, 86, 87, 88, 89, 162, 163, 165, 166, 167, 168, 169, 170, 243, 244, 245, 247, 248, 249, 250, 251, 324, 325, 326, 327, 329, 330, 331, 332, 405, 406, 407, 408, 409, 411, 412, 413, 486, 487, 488

Offset: 1

Clark Kimberling

Also: Numbers which, written in base 81, have only digits 0,...,8, and no two adjacent digits equal. - M. F. Hasler, Feb 03 2014

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

is_A043313(n)=(n=[n])&&!until(!n[1],((n=divrem(n[1],81))[2]<9 && n[1]%9!=n[2])||return) \\ M. F. Hasler, Feb 03 2014

cp's OEIS Frontend

A033014 Every run of digits of n in base 16 has length 2.

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A043307 a(n) = A033001(n)/4.

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

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

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

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

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A043309 a(n)=A033003(n)/6.

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A043310 a(n)=A033004(n)/7.

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A043311 a(n)=A033005(n)/8.

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