A334968 -id:A334968 - cp's OEIS frontend

A335525 Numbers k such that the k-th composition in standard order (A066099) avoids the pattern (1,2,2).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 1

Gus Wiseman, Jun 18 2020

nonn

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).

Wikipedia, Permutation pattern
Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid.
Gus Wiseman, Statistics, classes, and transformations of standard compositions

Patterns avoiding this pattern are counted by A001710 (by length).
Permutations of prime indices avoiding this pattern are counted by A335450.
These compositions are counted by A335473 (by sum).
The complement A335475 is the matching version.
The (2,2,1)-avoiding version is A335524.
Constant patterns are counted by A000005 and ranked by A272919.
Permutations are counted by A000142 and ranked by A333218.
Patterns are counted by A000670 and ranked by A333217.
Non-unimodal compositions are counted by A115981 and ranked by A335373.
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
Cf. A034691, A056986, A108917, A114994, A238279, A333224, A333257, A334968, A335446, A335456, A335458.

stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
Select[Range[0,100],!MatchQ[stc[#],{_,x_,_,y_,_,y_,_}/;x

A354907 Number of distinct sums of contiguous constant subsequences (partial runs) of the n-th composition in standard order.

Original entry on oeis.org

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

Offset: 0

Gus Wiseman, Jun 23 2022

nonn

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

Every sequence can be uniquely split into a sequence of non-overlapping runs. For example, the runs of (2,2,1,1,1,3,2,2) are ((2,2),(1,1,1),(3),(2,2)), with sums (4,3,3,4).

			Composition number 981 in standard order is (1,1,1,2,2,2,1), with partial runs (1), (2), (1,1), (2,2), (1,1,1), (2,2,2), with distinct sums {1,2,3,4,6}, so a(981) = 5.

Positions of 1's are A000051.
Positions of first appearances are A000079.
The standard compositions used here are A066099, run-sums A353847/A353932.
If we allow any subsequence we get A334968.
The case of full runs is A353849, firsts A246534.
A version for nonempty partitions is A353861, full A353835.
Counting all distinct runs (instead of their distinct sums) gives A354582.
A124767 counts runs in standard compositions.
A238279 and A333755 count compositions by number of runs.
A330036 counts distinct partial runs of prime indices, full A005811.
A351014 counts distinct runs of standard compositions, firsts A351015.
A353853-A353859 pertain to composition run-sum trajectory.
A353860 counts collapsible compositions.
A354584 lists run-sums of prime indices, rows ranked by A353832.
Cf. A029837, A124771, A274174, A333381, A334299, A353864.

stc[n_]:=Differences[Prepend[Join@@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
pre[y_]:=NestWhileList[Most,y,Length[#]>1&];
Table[Length[Union[Total/@Join@@pre/@Split[stc[n]]]],{n,0,100}]

A335488 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,1).

Original entry on oeis.org

3, 7, 10, 11, 13, 14, 15, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 35, 36, 39, 42, 43, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 99, 100, 101

Offset: 1

Gus Wiseman, Jun 18 2020

nonn

These are compositions with some part appearing more than once, or non-strict compositions.
A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).

			The sequence of terms together with the corresponding compositions begins:
   3: (1,1)
   7: (1,1,1)
  10: (2,2)
  11: (2,1,1)
  13: (1,2,1)
  14: (1,1,2)
  15: (1,1,1,1)
  19: (3,1,1)
  21: (2,2,1)
  22: (2,1,2)
  23: (2,1,1,1)
  25: (1,3,1)
  26: (1,2,2)
  27: (1,2,1,1)
  28: (1,1,3)

Wikipedia, Permutation pattern
Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid.
Gus Wiseman, Statistics, classes, and transformations of standard compositions

The complement A233564 is the avoiding version.
Patterns matching this pattern are counted by A019472 (by length).
Permutations of prime indices matching this pattern are counted by A335487.
These compositions are counted by A261982 (by sum).
Constant patterns are counted by A000005 and ranked by A272919.
Permutations are counted by A000142 and ranked by A333218.
Patterns are counted by A000670 and ranked by A333217.
Non-unimodal compositions are counted by A115981 and ranked by A335373.
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
The (1,1,1)-matching case is A335512.
Cf. A034691, A056986, A108917, A114994, A238279, A333224, A333257, A334968, A335456, A335458.

stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
Select[Range[0,100],MatchQ[stc[#],{_,x_,_,x_,_}]&]

A335512 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,1,1).

Original entry on oeis.org

7, 15, 23, 27, 29, 30, 31, 39, 42, 47, 51, 55, 57, 59, 60, 61, 62, 63, 71, 79, 85, 86, 87, 90, 91, 93, 94, 95, 99, 103, 106, 107, 109, 110, 111, 113, 115, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 135, 143, 151, 155, 157, 158, 159, 167, 170, 171

Offset: 1

Gus Wiseman, Jun 18 2020

nonn

These are compositions with some part appearing more than twice.
A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).

			The sequence of terms together with the corresponding compositions begins:
   7: (1,1,1)
  15: (1,1,1,1)
  23: (2,1,1,1)
  27: (1,2,1,1)
  29: (1,1,2,1)
  30: (1,1,1,2)
  31: (1,1,1,1,1)
  39: (3,1,1,1)
  42: (2,2,2)
  47: (2,1,1,1,1)
  51: (1,3,1,1)
  55: (1,2,1,1,1)
  57: (1,1,3,1)
  59: (1,1,2,1,1)
  60: (1,1,1,3)

Wikipedia, Permutation pattern
Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid.
Gus Wiseman, Statistics, classes, and transformations of standard compositions

The complement A335513 is the avoiding version.
Patterns matching this pattern are counted by A335508 (by length).
Permutations of prime indices matching this pattern are counted by A335510.
These compositions are counted by A335455 (by sum).
Constant patterns are counted by A000005 and ranked by A272919.
Permutations are counted by A000142 and ranked by A333218.
Patterns are counted by A000670 and ranked by A333217.
Non-unimodal compositions are counted by A115981 and ranked by A335373.
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
The (1,1)-matching version is A335488.
Cf. A034691, A056986, A114994, A238279, A334968, A335456, A335458.

stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
Select[Range[0,100],MatchQ[stc[#],{_,x_,_,x_,_,x_,_}]&]

A334300 Number of distinct nonempty subsequences (not necessarily contiguous) in the n-th composition in standard order (A066099).

Original entry on oeis.org

0, 1, 1, 2, 1, 3, 3, 3, 1, 3, 2, 5, 3, 6, 5, 4, 1, 3, 3, 5, 3, 5, 6, 7, 3, 6, 5, 9, 5, 9, 7, 5, 1, 3, 3, 5, 2, 7, 7, 7, 3, 7, 3, 8, 7, 11, 10, 9, 3, 6, 7, 9, 7, 10, 11, 12, 5, 9, 8, 13, 7, 12, 9, 6, 1, 3, 3, 5, 3, 7, 7, 7, 3, 5, 5, 11, 6, 13, 11, 9, 3, 7, 6

Offset: 0

Gus Wiseman, Jun 01 2020

Looking only at contiguous subsequences, or restrictions to a subinterval, gives A124770.

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

			Triangle begins:
  1
  1 2
  1 3 3 3
  1 3 2 5 3 6 5 4
  1 3 3 5 3 5 6 7 3 6 5 9 5 9 7 5
If the k-th composition in standard order is c, then we say that the STC-number of c is k. The n-th column below lists the STC-numbers of the nonempty subsequences of the composition with STC-number n:
  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
        1     2  2  3     4   2   5   4   6   6   7
              1  1  1     1       3   1   5   3   3
                                  2       3   2   1
                                  1       2   1
                                          1

John Tyler Rascoe, Table of n, a(n) for n = 0..8192

Row lengths are A011782.
Looking only at contiguous subsequences gives A124770.
The contiguous case with empty subsequences allowed is A124771.
Allowing empty subsequences gives A334299.
Compositions where every subinterval has a different sum are A333222.
Knapsack compositions are A333223.
Contiguous positive subsequence-sums are counted by A333224.
Contiguous subsequence-sums are counted by A333257.
Subsequence-sums are counted by A334968.
Cf. A000120, A029931, A048793, A066099, A070939, A108917, A325676, A334967.

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Table[Length[Union[Rest[Subsets[stc[n]]]]],{n,0,100}]

from itertools import combinations
def comp(n):
    # see A357625
    return
def A334300(n):
    A,C = set(),comp(n)
    c = range(len(C))
    for j in c:
        for k in combinations(c, j):
            A.add(tuple(C[i] for i in k))
    return len(A) # John Tyler Rascoe, Mar 12 2025

a(n) = A334299(n) - 1.

A335513 Numbers k such that the k-th composition in standard order (A066099) avoids the pattern (1,1,1).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 32, 33, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 58, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 88, 89

Offset: 1

Gus Wiseman, Jun 18 2020

nonn

These are compositions with no part appearing more than twice.
A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).

			The sequence of terms together with the corresponding compositions begins:
   0: ()         17: (4,1)      37: (3,2,1)
   1: (1)        18: (3,2)      38: (3,1,2)
   2: (2)        19: (3,1,1)    40: (2,4)
   3: (1,1)      20: (2,3)      41: (2,3,1)
   4: (3)        21: (2,2,1)    43: (2,2,1,1)
   5: (2,1)      22: (2,1,2)    44: (2,1,3)
   6: (1,2)      24: (1,4)      45: (2,1,2,1)
   8: (4)        25: (1,3,1)    46: (2,1,1,2)
   9: (3,1)      26: (1,2,2)    48: (1,5)
  10: (2,2)      28: (1,1,3)    49: (1,4,1)
  11: (2,1,1)    32: (6)        50: (1,3,2)
  12: (1,3)      33: (5,1)      52: (1,2,3)
  13: (1,2,1)    34: (4,2)      53: (1,2,2,1)
  14: (1,1,2)    35: (4,1,1)    54: (1,2,1,2)
  16: (5)        36: (3,3)      56: (1,1,4)

Wikipedia, Permutation pattern
Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid.
Gus Wiseman, Statistics, classes, and transformations of standard compositions

These compositions are counted by A232432 (by sum).
The (1,1)-avoiding version is A233564.
The complement A335512 is the matching version.
Constant patterns are counted by A000005 and ranked by A272919.
Permutations are counted by A000142 and ranked by A333218.
Patterns are counted by A000670 and ranked by A333217.
Patterns avoiding (1,1,1) are counted by A080599 (by length).
Non-unimodal compositions are counted by A115981 and ranked by A335373.
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
Permutations of prime indices avoiding (1,1,1) are counted by A335511.
Cf. A034691, A056986, A108917, A114994, A238279, A334968, A335456, A335458.

stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
Select[Range[0,100],!MatchQ[stc[#],{_,x_,_,x_,_,x_,_}]&]

A343943 Number of distinct possible alternating sums of permutations of the multiset of prime factors of n.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Aug 19 2021

nonn

First differs from A096825 at a(525) = 3, A096825(525) = 4.
First differs from A345926 at a(90) = 4, A345926(90) = 3.
The alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(i-1) y_i. Of course, the alternating sum of prime factors is also the reverse-alternating sum of reversed prime factors.
Also the number of distinct "sums of prime factors" of divisors d|n such that bigomega(d) = bigomega(n)/2 rounded up.

			The divisors of 525 with 2 prime factors are: 15, 21, 25, 35, with prime factors {3,5}, {3,7}, {5,5}, {5,7}, with distinct sums {8,10,12}, so a(525) = 3.

The half-length submultisets are counted by A114921.
Including all multisets of prime factors gives A305611(n) + 1.
The strict rounded version appears to be counted by A342343.
The version for prime indices instead of prime factors is A345926.
A000005 counts divisors, which add up to A000203.
A001414 adds up prime factors, row sums of A027746.
A056239 adds up prime indices, row sums of A112798.
A071321 gives the alternating sum of prime factors (reverse: A071322).
A097805 counts compositions by alternating (or reverse-alternating) sum.
A103919 counts partitions by sum and alternating sum (reverse: A344612).
A108917 counts knapsack partitions, ranked by A299702.
A276024 and A299701 count positive subset-sums of partitions.
A316524 gives the alternating sum of prime indices (reverse: A344616).
A334968 counts subsequence-sums of standard compositions.
Cf. A008549, A032443, A083399, A096825, A344609, A345957.

prifac[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
Table[Length[Union[Total/@Subsets[prifac[n],{Ceiling[PrimeOmega[n]/2]}]]],{n,100}]

from sympy import factorint
from sympy.utilities.iterables import multiset_combinations
def A343943(n):
    fs = factorint(n)
    return len(set(sum(d) for d in multiset_combinations(fs,(sum(fs.values())+1)//2))) # Chai Wah Wu, Aug 23 2021

A335279 Positions of first appearances in A124771 = number of distinct contiguous subsequences of compositions in standard order.

Original entry on oeis.org

0, 1, 3, 5, 11, 15, 23, 27, 37, 47, 55, 107, 111, 119, 155, 215, 223, 239, 411, 431, 471, 479, 495, 549, 631, 943, 951, 959, 991, 1647, 1887, 1967, 1983, 2015, 2543, 2935, 3703, 3807, 3935, 3967, 4031, 6639, 6895, 7407, 7871, 7903, 8063, 8127, 10207, 13279

Offset: 1

Gus Wiseman, Jun 03 2020

nonn

			The sequence together with the corresponding compositions begins:
     0: ()                215: (1,2,2,1,1,1)
     1: (1)               223: (1,2,1,1,1,1,1)
     3: (1,1)             239: (1,1,2,1,1,1,1)
     5: (2,1)             411: (1,3,1,2,1,1)
    11: (2,1,1)           431: (1,2,2,1,1,1,1)
    15: (1,1,1,1)         471: (1,1,2,2,1,1,1)
    23: (2,1,1,1)         479: (1,1,2,1,1,1,1,1)
    27: (1,2,1,1)         495: (1,1,1,2,1,1,1,1)
    37: (3,2,1)           549: (4,3,2,1)
    47: (2,1,1,1,1)       631: (3,1,1,2,1,1,1)
    55: (1,2,1,1,1)       943: (1,1,2,2,1,1,1,1)
   107: (1,2,2,1,1)       951: (1,1,2,1,2,1,1,1)
   111: (1,2,1,1,1,1)     959: (1,1,2,1,1,1,1,1,1)
   119: (1,1,2,1,1,1)     991: (1,1,1,2,1,1,1,1,1)
   155: (3,1,2,1,1)      1647: (1,3,1,2,1,1,1,1)
The subsequences for n = 0, 1, 3, 5, 11, 15, 23, 27 are the following (0 = empty partition):
  0  0  0   0   0    0     0     0     0    0
     1  1   1   1    1     1     1     1    1
        11  2   2    11    2     2     2    2
            21  11   111   11    11    3    11
                21   1111  21    12    21   21
                211        111   21    32   111
                           211   121   321  211
                           2111  211        1111
                                 1211       2111
                                            21111

Positions of first appearances in A124771.
Compositions where every subinterval has a different sum are A333222.
Knapsack compositions are A333223.
Cf. A000120, A003022, A029931, A066099, A070939, A124767, A124770, A325770, A334299, A334968.

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
seq=Table[Length[Union[ReplaceList[stc[n],{_,s___,_}:>{s}]]],{n,0,1000}];
Table[Position[seq,i][[1,1]]-1,{i,First/@Gather[seq]}]

A354908 Numbers k such that the k-th composition in standard order (graded reverse-lexicographic, A066099) is collapsible.

Original entry on oeis.org

1, 2, 3, 4, 7, 8, 10, 11, 14, 15, 16, 31, 32, 36, 39, 42, 43, 46, 47, 58, 59, 60, 62, 63, 64, 127, 128, 136, 138, 139, 142, 143, 168, 170, 171, 174, 175, 184, 186, 187, 190, 191, 232, 234, 235, 238, 239, 248, 250, 251, 254, 255, 256, 292, 295, 316, 319, 484

Offset: 1

Gus Wiseman, Jun 23 2022

nonn

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

If a collapse is an adding together of some partial run of an integer composition c, we say c is collapsible iff by some sequence of collapses it can be reduced to a single part. An example of such a sequence of collapses is (11132112) -> (332112) -> (33222) -> (6222) -> (66) -> (n), which shows that (11132112) is a collapsible composition of 12.

			The terms together with their corresponding compositions begin:
  1:(1)  2:(2)   4:(3)     8:(4)     16:(5)      32:(6)
         3:(11)  7:(111)  10:(22)    31:(11111)  36:(33)
                          11:(211)               39:(3111)
                          14:(112)               42:(222)
                          15:(1111)              43:(2211)
                                                 46:(2112)
                                                 47:(21111)
                                                 58:(1122)
                                                 59:(11211)
                                                 60:(1113)
                                                 62:(11112)
                                                 63:(111111)

The standard compositions used here are A066099, run-sums A353847/A353932.
The version for Heinz numbers of partitions is A300273, counted by A275870.
These compositions are counted by A353860.
A003242 counts anti-run compositions, ranked by A333489, complement A261983.
A011782 counts compositions.
A124767 counts runs in standard compositions.
A238279 and A333755 count compositions by number of runs.
A334968 counts distinct sums of subsequences of standard compositions.
A351014 counts distinct runs of standard compositions, firsts A351015.
A353853-A353859 pertain to composition run-sum trajectory.
A354582 counts distinct partial runs of standard compositions, sums A354907.
Cf. A005811, A029837, A072639, A124771, A274174, A318928, A333381, A353848, A353849, A353850.

repcams[q_List]:=repcams[q]=Union[{q},If[UnsameQ@@q,{},Union@@repcams/@Union[Insert[Drop[q,#],Plus@@Take[q,#],First[#]]&/@Select[Tuples[Range[Length[q]],2],And[Less@@#,SameQ@@Take[q,#]]&]]]];
stc[n_]:=Differences[Prepend[Join@@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Select[Range[0,100],MemberQ[repcams[stc[#]],{_}]&]

cp's OEIS Frontend

A335525 Numbers k such that the k-th composition in standard order (A066099) avoids the pattern (1,2,2).

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A354907 Number of distinct sums of contiguous constant subsequences (partial runs) of the n-th composition in standard order.

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A335488 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,1).

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A335512 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,1,1).

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A334300 Number of distinct nonempty subsequences (not necessarily contiguous) in the n-th composition in standard order (A066099).

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A335513 Numbers k such that the k-th composition in standard order (A066099) avoids the pattern (1,1,1).

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A343943 Number of distinct possible alternating sums of permutations of the multiset of prime factors of n.

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A335279 Positions of first appearances in A124771 = number of distinct contiguous subsequences of compositions in standard order.

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A354908 Numbers k such that the k-th composition in standard order (graded reverse-lexicographic, A066099) is collapsible.