A164707 -id:A164707 - cp's OEIS frontend

A383013 Number of integer partitions of n having a permutation with all equal run-lengths.

1, 1, 2, 3, 5, 6, 9, 11, 18, 21, 31, 38, 56, 67, 94, 121, 162, 199, 265, 330, 438, 543, 693, 859, 1103, 1353, 1702, 2097, 2619, 3194, 3972, 4821, 5943, 7206, 8796, 10632, 12938, 15536, 18794, 22539, 27133, 32374, 38827, 46175, 55134, 65421, 77751, 91951, 109011, 128482

Offset: 0

Gus Wiseman, Apr 12 2025

nonn

A partition of n counts towards a(n) if and only if #p + g >= 2*L where #p is the number of parts counted with multiplicity of the partition, g is the gcd of all the frequencies of every distinct part and L is the largest frequency of a part. - David A. Corneth, Apr 27 2025

			The partition (2,2,1,1,1,1) has permutation (1,1,2,2,1,1) with equal run-lengths (2,2,2) so is counted under a(8).
The a(1) = 1 through a(8) = 18 partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (21)   (22)    (32)     (33)      (43)       (44)
             (111)  (31)    (41)     (42)      (52)       (53)
                    (211)   (221)    (51)      (61)       (62)
                    (1111)  (311)    (222)     (322)      (71)
                            (11111)  (321)     (331)      (332)
                                     (411)     (421)      (422)
                                     (2211)    (511)      (431)
                                     (111111)  (3211)     (521)
                                               (22111)    (611)
                                               (1111111)  (2222)
                                                          (3221)
                                                          (3311)
                                                          (4211)
                                                          (22211)
                                                          (32111)
                                                          (221111)
                                                          (11111111)

David A. Corneth, Table of n, a(n) for n = 0..82

For distinct instead of equal run-lengths we have A239455, ranked by A351294.
The complement for distinct run-lengths is A351293, ranked by A351295.
The complement is counted by A382915, ranked by A382879, by signature A382914.
A000041 counts integer partitions, strict A000009.
A304442 counts partitions with equal run-sums, ranks A353833.
A329738 counts compositions with equal run-lengths, ranks A353744.
A329739 counts compositions with distinct run-lengths, ranks A351596.
A382857 counts permutations of prime indices with equal run-lengths, firsts A382878.
Cf. A003242, A047966, A164707, A238279, A351201, A351290, A351291, A353837, A353851, A382858.

Table[Length[Select[IntegerPartitions[n],Select[Permutations[#], SameQ@@Length/@Split[#]&]!={}&]],{n,0,15}]

More terms from Bert Dobbelaere, Apr 26 2025

A200649 Number of 1's in the Stolarsky representation of n.

Original entry on oeis.org

0, 1, 2, 1, 3, 2, 2, 4, 1, 3, 3, 3, 5, 2, 2, 4, 2, 4, 4, 4, 6, 1, 3, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 7, 2, 2, 4, 2, 4, 4, 4, 6, 2, 4, 4, 4, 6, 4, 4, 6, 4, 6, 6, 6, 8, 1, 3, 3, 3, 5, 3, 3, 5, 3, 5, 5, 5, 7, 3, 3, 5, 3, 5, 5, 5, 7, 3, 5, 5, 5, 7, 5, 5, 7, 5, 7, 7

Offset: 1

Casey Mongoven, Nov 19 2011

For the Stolarsky representation of n, see the C. Mongoven link.

Conjecture: a(n) is the length of row n-1 of A385886. To obtain it, first take maximal anti-run lengths of binary indices of each nonnegative integer (giving A384877), then remove all duplicate rows (giving A385886), and finally take the length of each remaining row. For sum instead of length we appear to have A200648. For runs minus 1 instead of anti-runs see A200650. - Gus Wiseman, Jul 21 2025

			The Stolarsky representation of 19 is 11101. This has 4 1's. So a(19) = 4.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Casey Mongoven, Description of Stolarsky Representations.

Cf. A072649, A130312, A135818, A200651.
For length instead of number of 1's we have A200648.
For 0's instead of 1's we have A200650.
Stolarsky representation is listed by A385888, ranks A200714.
A000120 counts 1's in binary expansion.
A384877 lists anti-run lengths of binary indices, duplicates removed A385886.
A384890 counts maximal anti-runs of binary indices, ranked by A385816.
Cf. A023758, A044813, A048793, A069010, A164707, A245562, A245563, A328592, A384893.

stol[n_] := stol[n] = If[n == 1, {}, If[n != Round[Round[n/GoldenRatio]*GoldenRatio], Join[stol[Floor[n/GoldenRatio^2] + 1], {0}], Join[stol[Round[n/GoldenRatio]], {1}]]];
a[n_] := Count[stol[n], 1]; Array[a, 100] (* Amiram Eldar, Jul 07 2023 *)

stol(n) = {my(phi=quadgen(5)); if(n==1, [], if(n != round(round(n/phi)*phi), concat(stol(floor(n/phi^2) + 1), [0]), concat(stol(round(n/phi)), [1])));}
a(n) = vecsum(stol(n)); \\ Amiram Eldar, Jul 07 2023

a(n) = a(n - A130312(n-1)) + (A072649(n-1) - A072649(n - A130312(n-1) - 1)) mod 2 for n > 2 with a(1) = 0, a(2) = 1. - Mikhail Kurkov, Oct 19 2021 [verification needed]

a(n) = A200648(n) - A200650(n). - Amiram Eldar, Jul 07 2023

More terms from Amiram Eldar, Jul 07 2023

A243815 Number of length n words on alphabet {0,1} such that the length of every maximal block of 0's (runs) is the same.

Original entry on oeis.org

1, 2, 4, 8, 14, 24, 39, 62, 97, 151, 233, 360, 557, 864, 1344, 2099, 3290, 5176, 8169, 12931, 20524, 32654, 52060, 83149, 133012, 213069, 341718, 548614, 881572, 1417722, 2281517, 3673830, 5918958, 9540577, 15384490, 24817031, 40045768, 64637963, 104358789

Offset: 0

Geoffrey Critzer, Jun 11 2014

nonn

Number of terms of A164710 with exactly n+1 binary digits. - Robert Israel, Nov 09 2015
From Gus Wiseman, Jun 23 2025: (Start)
This is the number of subsets of {1..n} with all equal lengths of runs of consecutive elements increasing by 1. For example, the runs of S = {1,2,5,6,8,9} are ((1,2),(5,6),(8,9)), with lengths (2,2,2), so S is counted under a(9). The a(0) = 1 through a(4) = 14 subsets are:
  {}  {}   {}     {}       {}
      {1}  {1}    {1}      {1}
           {2}    {2}      {2}
           {1,2}  {3}      {3}
                  {1,2}    {4}
                  {1,3}    {1,2}
                  {2,3}    {1,3}
                  {1,2,3}  {1,4}
                           {2,3}
                           {2,4}
                           {3,4}
                           {1,2,3}
                           {2,3,4}
                           {1,2,3,4}
(End)

			0110 is a "good" word because the length of both its runs of 0's is 1.
Words of the form 11...1 are good words because the condition is vacuously satisfied.
a(5) = 24 because there are 32 length 5 binary words but we do not count: 00010, 00101, 00110, 01000, 01001, 01100, 10010, 10100.

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A164710.
These subsets are ranked by A164707, complement A164708.
For distinct instead of equal lengths we have A384175, complement A384176.
For anti-runs instead of runs we have A384889, for partitions A384888.
For permutations instead of subsets we have A384892, distinct instead of equal A384891.
For partitions instead of subsets we have A384904, strict A384886.
The complement is counted by A385214.
A034839 counts subsets by number of maximal runs, for strict partitions A116674.
A049988 counts partitions with equal run-lengths, distinct A325325.
A329738 counts compositions with equal run-lengths, distinct A329739.
A384887 counts partitions with equal lengths of gapless runs, distinct A384884.
Cf. A010027, A044813, A069010, A268193, A383013, A384177, A384893.

a:= n-> 1 + add(add((d-> binomial(d+j, d))(n-(i*j-1))
          , j=1..iquo(n+1, i)), i=2..n+1):
seq(a(n), n=0..50);  # Alois P. Heinz, Jun 11 2014

nn=30;Prepend[Map[Total,Transpose[Table[Drop[CoefficientList[Series[ (1+x^k)/(1-x-x^(k+1))-1/(1-x),{x,0,nn}],x],1],{k,1,nn}]]],0]+1
Table[Length[Select[Subsets[Range[n]],SameQ@@Length/@Split[#,#2==#1+1&]&]],{n,0,10}] (* Gus Wiseman, Jun 23 2025 *)

A329860 Triangle read by rows where T(n,k) is the number of binary words of length n with cuts-resistance k.

Original entry on oeis.org

1, 0, 2, 0, 2, 2, 0, 2, 4, 2, 0, 2, 8, 4, 2, 0, 2, 12, 12, 4, 2, 0, 2, 20, 22, 14, 4, 2, 0, 2, 28, 48, 28, 16, 4, 2, 0, 2, 44, 84, 70, 32, 18, 4, 2, 0, 2, 60, 162, 136, 90, 36, 20, 4, 2, 0, 2, 92, 276, 298, 178, 110, 40, 22, 4, 2, 0, 2, 124, 500, 564, 432, 220, 132, 44, 24, 4, 2

Offset: 0

Gus Wiseman, Nov 23 2019

For the operation of shortening all runs by 1, cuts-resistance is defined to be the number of applications required to reach an empty word.

			Triangle begins:
   1
   0   2
   0   2   2
   0   2   4   2
   0   2   8   4   2
   0   2  12  12   4   2
   0   2  20  22  14   4   2
   0   2  28  48  28  16   4   2
   0   2  44  84  70  32  18   4   2
   0   2  60 162 136  90  36  20   4   2
   0   2  92 276 298 178 110  40  22   4   2
   0   2 124 500 564 432 220 132  44  24   4   2
Row n = 4 counts the following words:
  0101  0010  0001  0000
  1010  0011  0111  1111
        0100  1000
        0110  1110
        1001
        1011
        1100
        1101

Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003.

Column k = 2 appears to be 2 * A027383.
The version for runs-resistance is A319411 or A329767.
The cuts-resistance of the binary expansion of n is A319416(n).
The version for compositions is A329861.
Cf. A000975, A164707, A261983, A318928, A319420, A319421, A329738, A329865.

degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
Table[Length[Select[Tuples[{0,1},n],degdep[#]==k&]],{n,0,10},{k,0,n}]

For positive indices, T(n,k) = 2 * A319421(n,k).

A384879 Numbers whose binary indices have all distinct lengths of maximal anti-runs (increasing by more than 1).

Original entry on oeis.org

1, 2, 4, 5, 8, 9, 10, 11, 13, 16, 17, 18, 19, 20, 21, 22, 25, 26, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 49, 50, 52, 53, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 88, 97, 98, 100, 101, 104, 105, 106, 128, 129, 130

Offset: 1

Gus Wiseman, Jun 17 2025

nonn

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

			The binary indices of 813 are {1,3,4,6,9,10}, with maximal anti-runs ((1,3),(4,6,9),(10)), with lengths (2,3,1), so 813 is in the sequence.
The terms together with their binary expansions and binary indices begin:
    1:       1 ~ {1}
    2:      10 ~ {2}
    4:     100 ~ {3}
    5:     101 ~ {1,3}
    8:    1000 ~ {4}
    9:    1001 ~ {1,4}
   10:    1010 ~ {2,4}
   11:    1011 ~ {1,2,4}
   13:    1101 ~ {1,3,4}
   16:   10000 ~ {5}
   17:   10001 ~ {1,5}
   18:   10010 ~ {2,5}
   19:   10011 ~ {1,2,5}
   20:   10100 ~ {3,5}
   21:   10101 ~ {1,3,5}
   22:   10110 ~ {2,3,5}
   25:   11001 ~ {1,4,5}
   26:   11010 ~ {2,4,5}

Subsets of this type are counted by A384177, for runs A384175 (complement A384176).
These are the indices of strict rows in A384877, see A384878, A245563, A245562, A246029.
A000120 counts binary indices.
A098859 counts Wilf partitions (distinct multiplicities), complement A336866.
A356606 counts strict partitions without a neighborless part, complement A356607.
A384890 counts maximal anti-runs in binary indices, runs A069010.
Cf. A023758, A044813, A048793, A164707, A242882, A243815, A325325, A328592, A384879, A384884, A384886, A384893.

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
Select[Range[100],UnsameQ@@Length/@Split[bpe[#],#2!=#1+1&]&]

A319421 Triangle read by rows: T(n,k) (1 <= k <= n) = one-half of the number of binary vectors of length n and cuts-resistance k.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 6, 6, 2, 1, 1, 10, 11, 7, 2, 1, 1, 14, 24, 14, 8, 2, 1, 1, 22, 42, 35, 16, 9, 2, 1, 1, 30, 81, 68, 45, 18, 10, 2, 1, 1, 46, 138, 149, 89, 55, 20, 11, 2, 1, 1, 62, 250, 282, 216, 110, 66, 22, 12, 2, 1, 1, 94, 419, 577, 422, 285, 132, 78, 24, 13, 2, 1

Offset: 1

N. J. A. Sloane, Sep 23 2018

Cuts-resistance is defined in A319416.
This triangle summarizes the data shown in A319420.
Conjecture (Sloane): Sum_{i = 1..n} i * T(n,i) = A189391(n).

			Triangle begins:
   1
   1   1
   1   2   1
   1   4   2   1
   1   6   6   2   1
   1  10  11   7   2   1
   1  14  24  14   8   2   1
   1  22  42  35  16   9   2   1
   1  30  81  68  45  18  10   2   1
   1  46 138 149  89  55  20  11   2   1
   1  62 250 282 216 110  66  22  12   2   1
   1  94 419 577 422 285 132  78  24  13   2   1
Lenormand gives first 15 rows.
For example, the "1,2,1" row here refers to the 8 vectors of length 3. There are 2 vectors of cuts-resistance 1, namely 010 and 101 (see A319416), 4 vectors of cuts-resistance 2 (100,011,001,110), and 2 of cuts-resistance 3 (000 and 111). Halving these counts we get 1,2,1

Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003. Apparently unpublished. This is a scanned copy of the version that the author sent to me in 2003. See page 4.
N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

Row sums are A000079.
Column k = 2 appears to be A027383.
The version for runs-resistance is A319411 or A329767.
The version for compositions is A329861.
The cuts-resistance of the binary expansion of n is A319416(n).
Cf. A000975, A164707, A189391, A261983, A318921, A318928, A319420, A329738, A329860, A329865.

degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
Table[Length[Select[Tuples[{0,1},n],First[#]==1&°dep[#]==k&]],{n,8},{k,n}] (* Gus Wiseman, Nov 25 2019 *)

T(n,k) = A329860(n,k)/2. - Gus Wiseman, Nov 25 2019

A329865 Numbers whose binary expansion has the same runs-resistance as cuts-resistance.

Original entry on oeis.org

0, 8, 12, 14, 17, 24, 27, 28, 35, 36, 39, 47, 49, 51, 54, 57, 61, 70, 73, 78, 80, 99, 122, 130, 156, 175, 184, 189, 190, 198, 204, 207, 208, 215, 216, 226, 228, 235, 243, 244, 245, 261, 271, 283, 295, 304, 313, 321, 322, 336, 352, 367, 375, 378, 379, 380, 386

Offset: 1

Gus Wiseman, Nov 23 2019

nonn

For the operation of taking the sequence of run-lengths of a finite sequence, runs-resistance is defined to be the number of applications required to reach a singleton.

For the operation of shortening all runs by 1, cuts-resistance is defined to be the number of applications required to reach an empty word.

			The sequence of terms together with their binary expansions begins:
    0:
    8:      1000
   12:      1100
   14:      1110
   17:     10001
   24:     11000
   27:     11011
   28:     11100
   35:    100011
   36:    100100
   39:    100111
   47:    101111
   49:    110001
   51:    110011
   54:    110110
   57:    111001
   61:    111101
   70:   1000110
   73:   1001001
   78:   1001110
   80:   1010000
For example, 36 has runs-resistance 3 because we have (100100) -> (1212) -> (1111) -> (4), while the cuts-resistance is also 3 because we have (100100) -> (00) -> (0) -> ().
Similarly, 57 has runs-resistance 3 because we have (111001) -> (321) -> (111) -> (3), while the cuts-resistance is also 3 because we have (111001) -> (110) -> (1) -> ().

Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003.

Positions of 0's in A329867.
The version for runs-resistance equal to cuts-resistance minus 1 is A329866.
Compositions with runs-resistance equal to cuts-resistance are A329864.
Runs-resistance of binary expansion is A318928.
Cuts-resistance of binary expansion is A319416.
Compositions counted by runs-resistance are A329744.
Compositions counted by cuts-resistance are A329861.
Binary words counted by runs-resistance are A319411 and A329767.
Binary words counted by cuts-resistance are A319421 and A329860.
Cf. A000975, A003242, A107907, A164707, A319420, A329738, A329868.

runsres[q_]:=Length[NestWhileList[Length/@Split[#]&,q,Length[#]>1&]]-1;
degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
Select[Range[0,100],#==0||runsres[IntegerDigits[#,2]]==degdep[IntegerDigits[#,2]]&]

A385886 Irregular triangle read by rows listing the lengths of maximal anti-runs (sequences of distinct consecutive elements increasing by more than 1) of binary indices, duplicate rows removed.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 1, 1, 2, 1

Offset: 0

Gus Wiseman, Jul 14 2025

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

This is the triangle A384877, except all duplicates after the first instance of each composition are removed. It lists all compositions in order of their first appearance as a row of A384877.

			The binary indices of 27 are {1,2,4,5}, with maximal anti-runs ((1),(2,4),(5)), with lengths (1,2,1). After removing duplicates, this is our row 10.
The binary indices of 53 are {1,3,5,6}, with maximal anti-runs ((1,3,5),(6)), with lengths (3,1). After removing duplicates, this is our row 16.
Triangle begins:
   0: .
   1: 1
   2: 1 1
   3: 2
   4: 1 1 1
   5: 1 2
   6: 2 1
   7: 1 1 1 1
   8: 3
   9: 1 1 2
  10: 1 2 1
  11: 2 1 1
  12: 1 1 1 1 1
  13: 1 3
  14: 2 2
  15: 1 1 1 2
  16: 3 1
  17: 1 1 2 1
  18: 1 2 1 1
  19: 2 1 1 1
  20: 1 1 1 1 1 1

In the following references, "before" is short for "before removing duplicate rows".
Positions of singleton rows appear to be A001906 = A055588 - 1.
Positions of rows of the form (1,1,...) appear to be A001911-2, before A023758.
Row sums appear to be A200648, before A000120.
Row lengths appear to be A200649, before A384890.
Standard composition numbers of each row appear to be A348366.
Before we had A384877, ranks A385816, firsts A052499.
For runs instead of anti-runs we have A385817, see A245563, A245562, A246029.
Cf. A044813, A048793, A069010, A164707, A242882, A328592, A384175, A384177, A384878, A384879, A384893.

DeleteDuplicates[Table[Length/@Split[Join@@Position[Reverse[IntegerDigits[n,2]],1],#2!=#1+1&],{n,0,100}]]

A329862 Positive integers whose binary expansion has cuts-resistance 2.

Original entry on oeis.org

3, 4, 6, 9, 11, 12, 13, 18, 19, 20, 22, 25, 26, 37, 38, 41, 43, 44, 45, 50, 51, 52, 53, 74, 75, 76, 77, 82, 83, 84, 86, 89, 90, 101, 102, 105, 106, 149, 150, 153, 154, 165, 166, 169, 171, 172, 173, 178, 179, 180, 181, 202, 203, 204, 205, 210, 211, 212, 213

Offset: 1

Gus Wiseman, Nov 23 2019

nonn

For the operation of shortening all runs by 1, cuts-resistance is defined to be the number of applications required to reach an empty word.

			The sequence of terms together with their binary expansions begins:
   3:      11
   4:     100
   6:     110
   9:    1001
  11:    1011
  12:    1100
  13:    1101
  18:   10010
  19:   10011
  20:   10100
  22:   10110
  25:   11001
  26:   11010
  37:  100101
  38:  100110
  41:  101001
  43:  101011
  44:  101100
  45:  101101
  50:  110010

Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003.

Positions of 2's in A319416.
Numbers whose binary expansion has cuts-resistance 1 are A000975.
Binary words with cuts-resistance 2 are conjectured to be A027383.
Compositions with cuts-resistance 2 are A329863.
Cuts-resistance of binary expansion without first digit is A319420.
Binary words counted by cuts-resistance are A319421 and A329860.
Compositions counted by cuts-resistance are A329861.
Cf. A107907, A114901, A164707, A318928, A319411, A329745, A329865, A329866.

degdep[q_]:=Length[NestWhileList[Join@@Rest/@Split[#]&,q,Length[#]>0&]]-1;
Select[Range[100],degdep[IntegerDigits[#,2]]==2&]

A164710 A positive integer n is included if all runs of 0's in binary n are of the same length.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 39, 42, 43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 71, 73, 76, 79, 85, 86, 87, 90, 91, 93, 94, 95, 96, 97, 99, 100

Offset: 1

Leroy Quet, Aug 23 2009

Clarification: A binary number consists of "runs" completely of 1's alternating with runs completely of 0's. No two or more runs all of the same digit are adjacent.
This sequence contains in part positive integers that each contain one run of 0's. For those members of this sequence each with at least two runs of 0's, see A164712.
Number of terms with n binary digits is A243815(n-1). - Robert Israel, Nov 09 2015

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A164707, A164711, A164712, A243815.

isA164710 := proc(n) local bdg,arl,lset ; bdg := convert(n,base,2) ; lset := {} ; arl := -1 ; for p from 1 to nops(bdg) do if op(p,bdg) = 0 then if p = 1 then arl := 1 ; else arl := arl+1 ; end if; else if arl > 0 then lset := lset union {arl} ; end if; arl := 0 ; end if; end do ; if arl > 0 then lset := lset union {arl} ; end if; return (nops(lset) <= 1 ); end proc: for n from 1 to 300 do if isA164710(n) then printf("%d,",n) ; end if; end do; # R. J. Mathar, Feb 27 2010
F:= proc(d)
  local res,r,m,e,C,M;
  res:= [1$d];
  for r from 1 to floor(d/2) do
    for m from 1 to floor(d/r)-1 do
       e:= d - r*(m+1);
       for C in combinat:-choose(e+r,e) do
         M:= subsop(op(map(`=`,C,1)),[0$(e+r)]);
         res:= res, subs(0 = (1,0$m), M);
       od
    od
  od;
  sort(map(t -> add(t[-i]*2^(i-1),i=1..d), [res]));
end proc:
N:= 10: # to get all terms < 2^N
map(op,[seq(F(d),d=1..N)]); # Robert Israel, Nov 09 2015

Select[Range@ 100, SameQ @@ Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 0 &]] &] (* Michael De Vlieger, Aug 20 2017 *)

foreach(1..100){
    %runs=();
    $runs{$}++ foreach split /1+/, sprintf("%b",$);
    delete $runs{''};
    print "$_, " if 1>=keys(%runs);
}
# Ivan Neretin, Nov 09 2015

Terms beyond 39 by R. J. Mathar, Feb 27 2010

cp's OEIS Frontend

A383013 Number of integer partitions of n having a permutation with all equal run-lengths.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A200649 Number of 1's in the Stolarsky representation of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A243815 Number of length n words on alphabet {0,1} such that the length of every maximal block of 0's (runs) is the same.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A329860 Triangle read by rows where T(n,k) is the number of binary words of length n with cuts-resistance k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A384879 Numbers whose binary indices have all distinct lengths of maximal anti-runs (increasing by more than 1).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A319421 Triangle read by rows: T(n,k) (1 <= k <= n) = one-half of the number of binary vectors of length n and cuts-resistance k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A329865 Numbers whose binary expansion has the same runs-resistance as cuts-resistance.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A385886 Irregular triangle read by rows listing the lengths of maximal anti-runs (sequences of distinct consecutive elements increasing by more than 1) of binary indices, duplicate rows removed.

Views

Author