A073491 -id:A073491 - cp's OEIS frontend

A356603 Position in A356226 of first appearance of the n-th composition in standard order (row n of A066099).

1, 2, 4, 10, 8, 20, 50, 110, 16, 40, 100, 220, 250, 550, 1210, 1870, 32, 80, 200, 440, 500, 1100, 2420, 3740, 1250, 2750, 6050, 9350, 13310, 20570, 31790, 43010, 64, 160, 400, 880, 1000, 2200, 4840, 7480, 2500, 5500, 12100, 18700, 26620, 41140, 63580, 86020

Offset: 0

Gus Wiseman, Aug 30 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.

The image consists of all numbers whose prime indices are odd and cover an initial interval of odd positive integers.

			The terms together with their prime indices begin:
      1: {}
      2: {1}
      4: {1,1}
     10: {1,3}
      8: {1,1,1}
     20: {1,1,3}
     50: {1,3,3}
    110: {1,3,5}
     16: {1,1,1,1}
     40: {1,1,1,3}
    100: {1,1,3,3}
    220: {1,1,3,5}
    250: {1,3,3,3}
    550: {1,3,3,5}
   1210: {1,3,5,5}
   1870: {1,3,5,7}

Gus Wiseman, Statistics, classes, and transformations of standard compositions

See link for sequences related to standard compositions.
The partitions with these Heinz numbers are counted by A053251.
A subset of A066208 (numbers with all odd prime indices).
Up to permutation, these are the positions of first appearances of rows in A356226. Other statistics are:
- length: A287170, firsts A066205
- minimum: A356227
- maximum: A356228
- bisected length: A356229
- standard composition: A356230
- Heinz number: A356231
The sorted version is A356232.
An ordered version is counted by A356604.
A001221 counts distinct prime factors, sum A001414.
A073491 lists numbers with gapless prime indices, complement A073492.
Cf. A000005, A001222, A055932, A061395, A073493, A132747, A137921, A193829, A286470, A356224, A356237.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
stcinv[q_]:=1/2 Total[2^Accumulate[Reverse[q]]];
mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
sq=stcinv/@Table[Length/@Split[primeMS[n],#1>=#2-1&],{n,1000}];
Table[Position[sq,k][[1,1]],{k,0,mnrm[Rest[sq]]}]

A384887 Number of integer partitions of n with all equal lengths of maximal gapless runs (decreasing by 0 or 1).

Original entry on oeis.org

1, 1, 2, 3, 5, 6, 9, 10, 14, 18, 21, 26, 35, 39, 46, 58, 68, 79, 97, 111, 131, 155, 177, 206, 246, 278, 318, 373, 423, 483, 563, 632, 722, 827, 931, 1058, 1209, 1354, 1528, 1736, 1951, 2188, 2475, 2762, 3097, 3488, 3886, 4342, 4876, 5414, 6038, 6741, 7482

Offset: 0

Gus Wiseman, Jun 15 2025

nonn

			The partition y = (6,5,5,5,3,3,2,1) has maximal gapless runs ((6,5,5,5),(3,3,2,1)), with lengths (4,4), so y is counted under a(30).
The a(1) = 1 through a(8) = 14 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)  (2111)   (222)     (322)      (71)
                            (11111)  (321)     (2221)     (332)
                                     (2211)    (3211)     (2222)
                                     (21111)   (22111)    (3221)
                                     (111111)  (211111)   (3311)
                                               (1111111)  (22211)
                                                          (32111)
                                                          (221111)
                                                          (2111111)
                                                          (11111111)

The strict case is A384886, distinct A384178.
For distinct instead of equal lengths we have A384884.
For anti-runs instead of runs we have A384888, distinct A384885.
For subsets instead of strict partitions we have A243815.
Without counting decreases by 0 we get A384904.
A000041 counts integer partitions, strict A000009.
A007690 counts partitions with no singletons, complement A183558.
A034296 counts flat or gapless partitions, ranks A066311 or A073491.
A098859 counts Wilf partitions (distinct multiplicities), complement A336866.
A355394 counts partitions without a neighborless part, singleton case A355393.
A356236 counts partitions with a neighborless part, singleton case A356235.
A356606 counts strict partitions without a neighborless part, complement A356607.
Cf. A008284, A044813, A047993, A325324, A325325, A356226, A356230, A356233, A356234, A384175, A384177, A384880.

Table[Length[Select[IntegerPartitions[n],SameQ@@Length/@Split[#,#2>=#1-1&]&]],{n,0,15}]

A277020 Unary-binary representation of Stern polynomials: a(n) = A156552(A260443(n)).

Original entry on oeis.org

0, 1, 2, 5, 4, 13, 10, 21, 8, 45, 26, 93, 20, 109, 42, 85, 16, 173, 90, 477, 52, 957, 186, 733, 40, 749, 218, 1501, 84, 877, 170, 341, 32, 685, 346, 3549, 180, 12221, 954, 7133, 104, 14269, 1914, 49021, 372, 28605, 1466, 5853, 80, 5869, 1498, 30685, 436, 61373, 3002, 23517, 168, 12013, 1754, 24029, 340, 7021, 682, 1365

Offset: 0

Antti Karttunen, Oct 07 2016

Sequence encodes Stern polynomials (see A125184, A260443) with "unary-binary method" where any nonzero coefficient c > 0 is encoded as a run of c 1-bits, separated from neighboring 1-runs by exactly one zero (this follows because A260442 is a subsequence of A073491). See the examples.

Terms which are not multiples of 4 form a subset of A003754, or in other words, each term is 2^k * {a term from a certain subsequence of A247648}, which subsequence remains to be determined.

			n    Stern polynomial       Encoded as              a(n)
                            "unary-binary" number   (-> decimal)
----------------------------------------------------------------
0    B_0(x) = 0                     "0"               0
1    B_1(x) = 1                     "1"               1
2    B_2(x) = x                    "10"               2
3    B_3(x) = x + 1               "101"               5
4    B_4(x) = x^2                 "100"               4
5    B_5(x) = 2x + 1             "1101"              13
6    B_6(x) = x^2 + x            "1010"              10
7    B_7(x) = x^2 + x + 1       "10101"              21
8    B_8(x) = x^3                "1000"               8
9    B_9(x) = x^2 + 2x + 1     "101101"              45

Antti Karttunen, Table of n, a(n) for n = 0..8191
Index entries for sequences related to binary expansion of n

Cf. A087808 (a left inverse), A156552, A260443, A277189 (odd bisection).

Cf. also A000079, A000120, A000225, A002450, A002487, A003754, A073491, A247648, A260442, A277010, A277012, A276081.

(define (A277020 n) (A156552 (A260443 n)))
;; Another implementation, more practical to run:
(define (A277020 n) (list_of_numbers_to_unary_binary_representation (A260443as_index_lists n)))
(definec (A260443as_index_lists n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_index_lists (/ n 2)))) (else (add_two_lists (A260443as_index_lists (/ (- n 1) 2)) (A260443as_index_lists (/ (+ n 1) 2))))))
(define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))
(define (list_of_numbers_to_unary_binary_representation nums) (let loop ((s 0) (nums nums) (b 1)) (cond ((null? nums) s) (else (loop (+ s (* (A000225 (car nums)) b)) (cdr nums) (* (A000079 (+ 1 (car nums))) b))))))

a(n) = A156552(A260443(n)).
Other identities. For all n >= 0:
A087808(a(n)) = n.
A000120(a(n)) = A002487(n).
a(2n) = 2*a(n).
a(2^n) = 2^n.
a(A000225(n)) = A002450(n).

A356227 Smallest size of a maximal gapless submultiset of the prime indices of n.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Aug 13 2022

nonn

A sequence is gapless if it covers an unbroken interval of positive integers. For example, the multiset {2,3,5,5,6,9} has three maximal gapless submultisets: {2,3}, {5,5,6}, {9}.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

			The prime indices of 18564 are {1,1,2,4,6,7}, with maximal gapless submultisets {1,1,2}, {4}, {6,7}, so a(18564) = 1.

Positions of first appearances are A000079.
The maximal gapless submultisets are counted by A287170, firsts A066205.
These are the row-minima of A356226, firsts A356232.
The greatest instead of smallest size is A356228.
A001221 counts distinct prime factors, with sum A001414.
A001222 counts prime factors with multiplicity.
A001223 lists the prime gaps, reduced A028334.
A003963 multiplies together the prime indices of n.
A056239 adds up prime indices, row sums of A112798.
A073491 lists numbers with gapless prime indices, cf. A073492-A073495.
A356224 counts even gapless divisors, complement A356225.
Cf. A000005, A055874, A060680-A060683, A132747, A132881, A137921, A193829, A286470, A356229.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[If[n==1,0,Min@@Length/@Split[primeMS[n],#1>=#2-1&]],{n,100}]

a(n) = A333768(A356230(n)).

a(n) = A055396(A356231(n)).

A356841 Numbers k such that the k-th composition in standard order covers an interval of positive integers (gapless).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 18, 20, 21, 22, 23, 26, 27, 29, 30, 31, 32, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 50, 52, 53, 54, 55, 58, 59, 61, 62, 63, 64, 68, 72, 74, 75, 77, 78, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 101

Offset: 1

Gus Wiseman, Aug 31 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.

			The terms and their corresponding standard compositions begin:
   0: ()
   1: (1)
   2: (2)
   3: (1,1)
   4: (3)
   5: (2,1)
   6: (1,2)
   7: (1,1,1)
   8: (4)
  10: (2,2)
  11: (2,1,1)
  13: (1,2,1)
  14: (1,1,2)
  15: (1,1,1,1)
  16: (5)
  18: (3,2)
  20: (2,3)
  21: (2,2,1)

Gus Wiseman, Statistics, classes, and transformations of standard compositions

See link for sequences related to standard compositions.
An unordered version is A073491, complement A073492.
These compositions are counted by A107428.
The complement is A356842.
The non-initial case is A356843, unordered A356845.
A356230 ranks gapless factorization lengths, firsts A356603.
A356233 counts factorizations into gapless numbers.
A356844 ranks compositions with at least one 1.
Cf. A053251, A055932, A073493, A132747, A137921, A286470, A356224/A356225.

nogapQ[m_]:=m=={}||Union[m]==Range[Min[m],Max[m]];
stc[n_]:=Differences[Prepend[Join@@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
Select[Range[0,100],nogapQ[stc[#]]&]

A365920 Greatest non-subset-sum of the prime indices of n, or 0 if there is none.

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 3, 0, 3, 2, 4, 0, 5, 3, 4, 0, 6, 0, 7, 0, 5, 4, 8, 0, 5, 5, 5, 3, 9, 0, 10, 0, 6, 6, 6, 0, 11, 7, 7, 0, 12, 0, 13, 4, 6, 8, 14, 0, 7, 5, 8, 5, 15, 0, 7, 0, 9, 9, 16, 0, 17, 10, 7, 0, 8, 4, 18, 6, 10, 6, 19, 0, 20, 11, 7, 7, 8, 5, 21, 0, 7, 12

Offset: 1

Gus Wiseman, Sep 30 2023

nonn

This is the greatest element of {0,...,A056239(n)} that is not equal to A056239(d) for any divisor d|n, d>1. This definition is analogous to the Frobenius number of a numerical semigroup (see link), but it looks only at submultisets of a finite multiset, not all multisets of elements of a set.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

			The prime indices of 156 are {1,1,2,6}, with subset-sums 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, so a(156) = 5.

Steven R. Finch, Monoids of natural numbers, March 17, 2009.

For binary indices instead of sums we have A063250.
Positions of first appearances > 2 are A065091.
Zeros are A325781, nonzeros A325798.
For prime indices instead of sums we have A339662, minimum A257993.
For least instead of greatest non-subset-sum we have A366128.
A055932 lists numbers whose prime indices cover an initial interval.
A056239 adds up prime indices, row sums of A112798.
A073491 lists numbers with gap-free prime indices.
A238709/A238710 count partitions by least/greatest difference.
A342050/A342051 have prime indices with odd/even least gap.
Cf. A001223, A001522, A005117, A079068, A098743, A264401, A286469 or A286470, A339737, A339886.

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
nmz[y_]:=Complement[Range[Total[y]],Total/@Subsets[y]];
Table[Max@@Prepend[nmz[prix[n]],0],{n,100}]

A384885 Number of integer partitions of n with all distinct lengths of maximal anti-runs (decreasing by more than 1).

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 4, 6, 8, 9, 13, 15, 18, 22, 28, 31, 38, 45, 53, 62, 74, 86, 105, 123, 146, 171, 208, 242, 290, 340, 399, 469, 552, 639, 747, 862, 999, 1150, 1326, 1514, 1736, 1979, 2256, 2560, 2909, 3283, 3721, 4191, 4726, 5311, 5973, 6691, 7510, 8396, 9395

Offset: 0

Gus Wiseman, Jun 13 2025

nonn

			The partition y = (8,6,3,3,3,1) has maximal anti-runs ((8,6,3),(3),(3,1)), with lengths (3,1,2), so y is counted under a(24).
The partition z = (8,6,5,3,3,1) has maximal anti-runs ((8,6),(5,3),(3,1)), with lengths (2,2,2), so z is not counted under a(26).
The a(1) = 1 through a(9) = 9 partitions:
  (1)  (2)  (3)  (4)    (5)      (6)      (7)      (8)      (9)
                 (3,1)  (4,1)    (4,2)    (5,2)    (5,3)    (6,3)
                        (3,1,1)  (5,1)    (6,1)    (6,2)    (7,2)
                                 (4,1,1)  (3,3,1)  (7,1)    (8,1)
                                          (4,2,1)  (4,2,2)  (4,4,1)
                                          (5,1,1)  (4,3,1)  (5,2,2)
                                                   (5,2,1)  (5,3,1)
                                                   (6,1,1)  (6,2,1)
                                                            (7,1,1)

For subsets instead of strict partitions we have A384177, for runs A384175.
The strict case is A384880.
For runs instead of anti-runs we have A384884, strict A384178.
For equal instead of distinct lengths we have A384888, for runs A384887.
A000041 counts integer partitions, strict A000009.
A007690 counts partitions with no singletons, complement A183558.
A034296 counts flat or gapless partitions, ranks A066311 or A073491.
A098859 counts Wilf partitions (distinct multiplicities), complement A336866.
A239455 counts Look-and-Say or section-sum partitions, ranks A351294 or A381432.
A355394 counts partitions without a neighborless part, singleton case A355393.
A356236 counts partitions with a neighborless part, singleton case A356235.
A356606 counts strict partitions without a neighborless part, complement A356607.
Cf. A008284, A047966, A242882, A287170, A325324, A325325, A329739, A356226, A356230, A356234, A384886.

Table[Length[Select[IntegerPartitions[n],UnsameQ@@Length/@Split[#,#2<#1-1&]&]],{n,0,15}]

A325161 Nonprime squarefree numbers not divisible by any two consecutive primes.

Original entry on oeis.org

1, 10, 14, 21, 22, 26, 33, 34, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 95, 106, 110, 111, 115, 118, 119, 122, 123, 129, 130, 133, 134, 141, 142, 145, 146, 155, 158, 159, 161, 166, 170, 177, 178, 182, 183, 185, 187, 190, 194, 201

Offset: 1

Gus Wiseman, Apr 05 2019

nonn

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of non-singleton integer partitions into distinct non-consecutive parts (counted by A003114 minus 1).

			The sequence of terms together with their prime indices begins:
   1: {}
  10: {1,3}
  14: {1,4}
  21: {2,4}
  22: {1,5}
  26: {1,6}
  33: {2,5}
  34: {1,7}
  38: {1,8}
  39: {2,6}
  46: {1,9}
  51: {2,7}
  55: {3,5}
  57: {2,8}
  58: {1,10}
  62: {1,11}
  65: {3,6}
  69: {2,9}
  74: {1,12}
  82: {1,13}

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001227, A003114, A005117, A025157, A034296, A056239, A073485, A073491, A089995, A112798, A116931, A319630, A325160, A325162.

Select[Range[100],!PrimeQ[#]&&Min@@Differences[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]>1&]

A384881 Triangle read by rows where T(n,k) is the number of integer partitions of n with k maximal runs of consecutive parts decreasing by 1.

Original entry on oeis.org

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

Offset: 0

Gus Wiseman, Jun 25 2025

			The partition (5,4,2,1,1) has maximal runs ((5,4),(2,1),(1)) so is counted under T(13,3) = 23.
Row n = 9 counts the following partitions:
  9    63    333    6111    33111   411111   3111111   111111111
  54   72    441    22221   51111   2211111  21111111
  432  81    522    42111   222111
       621   531    321111
       3321  711
             3222
             4221
             4311
             5211
             32211
Triangle begins:
  1
  0  1
  0  1  1
  0  2  0  1
  0  1  3  0  1
  0  2  2  2  0  1
  0  2  3  3  2  0  1
  0  2  5  3  2  2  0  1
  0  1  8  4  4  2  2  0  1
  0  3  5 10  4  3  2  2  0  1
  0  2  9  9  9  5  3  2  2  0  1
  0  2 11 13  9  9  4  3  2  2  0  1
  0  2 13 15 17  8 10  4  3  2  2  0  1
  0  2 14 23 16 17  8  9  4  3  2  2  0  1
  0  2 16 26 26 19 16  9  9  4  3  2  2  0  1
  0  4 13 37 32 26 19 16  8  9  4  3  2  2  0  1

John Tyler Rascoe, Rows n = 0..100, flattened

Row sums are A000041.
Column k = 1 is A001227.
For distinct parts instead of maximal runs we have A116608.
The strict case appears to be A116674.
For anti-runs instead of runs we have A268193.
Partitions with distinct runs of this type are counted by A384882, gapless A384884.
For prime indices see A385213, A287170, A066205, A356229.
A007690 counts partitions with no singletons, complement A183558.
A034296 counts flat or gapless partitions, ranks A066311 or A073491.
Cf. A000009, A000217, A008284, A047966, A047993, A098859, A325325, A375136, A384887.

Table[Length[Select[IntegerPartitions[n],Length[Split[#,#1==#2+1&]]==k&]],{n,0,10},{k,0,n}]

tri(n) = {(n*(n+1)/2)}
B_list(N) = {my(v = vector(N, i, 0)); v[1] = q*t; for(m=2,N, v[m] = t * (q^tri(m) + sum(i=1,m-1, q^tri(i) * v[m-i] * (q^((m-i)*(i-1))/(1 - q^(m-i)) - q^((m-i)*i) + O('q^(N-tri(i)+1)))))); v}
A_qt(max_row) = {my(N = max_row+1, B = B_list(N), g = 1 + sum(m=1,N, B[m]/(1 - q^m)) + O('q^(N+1))); vector(N, n, Vecrev(polcoeff(g, n-1)))} \\ John Tyler Rascoe, Aug 18 2025

G.f.: 1 + Sum_{m>0} B(m,q,t)/(1 - q^m) where B(m,q,t) = t * (q^tri(m) + Sum_{i=1..m-1} q^tri(i) * B(m-i,q,t) * ((q^((m-i)*(i-1))/(1 - q^(m-i))) - q^((m-i)*i))) and tri(n) = A000217(n). - John Tyler Rascoe, Aug 18 2025

A133813 Numbers that are primally tight and have strictly descending powers.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 23, 24, 25, 27, 29, 31, 32, 37, 41, 43, 45, 47, 48, 49, 53, 59, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 96, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 135, 137, 139, 144, 149, 151, 157, 163, 167, 169, 173, 175

Offset: 1

Olivier Gérard, Sep 23 2007

nonn

All numbers of the form p_1^k1*p_2^k2*...*p_n^k_n, where k1 > k2 > ... > k_n and the p_i are n successive primes.
Subset of A073491, A133812.
Differs from A085233 starting n=22.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A025487, A087980, A073491, A133808-A133812.

Cf. A027748, A124010, A049084, A020639, A000040, A087980.

import Data.List (isPrefixOf)
a133813 n = a133813_list !! (n-1)
a133813_list = 1 : filter f [2..] where
   f x = isPrefixOf ps (dropWhile (< a020639 x) a000040_list) &&
           all (< 0) (zipWith (-) (tail es) es)
         where ps = a027748_row x; es = a124010_row x
-- Reinhard Zumkeller, Apr 14 2015

A049084(A027748(a(n),k+1)) = A049084(A027748(a(n),k)) + 1 and A124010(a(n),k+1) < A124010(a(n),k), 1 <= k < A001221(a(n)). - Reinhard Zumkeller, Apr 14 2015

cp's OEIS Frontend

A356603 Position in A356226 of first appearance of the n-th composition in standard order (row n of A066099).

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A384887 Number of integer partitions of n with all equal lengths of maximal gapless runs (decreasing by 0 or 1).

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A277020 Unary-binary representation of Stern polynomials: a(n) = A156552(A260443(n)).

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A356227 Smallest size of a maximal gapless submultiset of the prime indices of n.

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A356841 Numbers k such that the k-th composition in standard order covers an interval of positive integers (gapless).

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A365920 Greatest non-subset-sum of the prime indices of n, or 0 if there is none.

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A384885 Number of integer partitions of n with all distinct lengths of maximal anti-runs (decreasing by more than 1).

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A325161 Nonprime squarefree numbers not divisible by any two consecutive primes.

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A384881 Triangle read by rows where T(n,k) is the number of integer partitions of n with k maximal runs of consecutive parts decreasing by 1.

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