A377093 -id:A377093 - cp's OEIS frontend

A377094 Inverse permutation to A377093.

1, 2, 4, 3, 7, 5, 12, 19, 6, 8, 27, 38, 50, 13, 9, 20, 63, 80, 98, 10, 14, 28, 117, 21, 11, 51, 140, 15, 167, 196, 226, 22, 29, 64, 16, 39, 257, 99, 52, 23, 294, 17, 335, 30, 378, 118, 423, 24, 18, 470, 65, 53, 520, 81, 31, 25, 100, 168, 573, 40, 632, 227, 693

Offset: 1

Rémy Sigrist, Oct 16 2024

nonn

			A377093(42) = 84, so a(84) = 42.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C++ program
Index entries for sequences that are permutations of the natural numbers

Cf. A377093.

from itertools import count, islice
def agen(): # generator of terms; uses A377093gen() in A377093
    adict, n = dict(), 1
    for k, v in enumerate(A377093gen(), 1):
        if v not in adict:
            adict[v] = k
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 63))) # Michael S. Branicky, Oct 16 2024

a(n) <= (n-1)*n/2 + 1. - Michael S. Branicky, Oct 16 2024

A376903 Lexicographically earliest sequence of distinct positive integers with a(1) multiples of 1 followed by a(2) multiples of 2 etc.

Original entry on oeis.org

1, 2, 4, 3, 6, 9, 12, 8, 16, 20, 5, 10, 15, 25, 30, 35, 18, 24, 36, 42, 48, 54, 60, 66, 72, 7, 14, 21, 28, 49, 56, 63, 70, 77, 84, 91, 98, 32, 40, 64, 80, 88, 96, 104, 112, 27, 45, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 50, 100, 110, 120

Offset: 1

Rémy Sigrist, Oct 08 2024

This sequence combines features of Golomb's sequence (A001462) and A075383.
This sequence is a permutation of the positive integers with inverse A376904.
This sequence can also be seen as an irregular table whose n-th row contains a(n) multiples of n.

			The first terms/rows are:
  n  a(n)  n-th row
  -  ----  ---------------------------------------------
  1     1  1
  2     2  2, 4
  3     4  3, 6, 9, 12
  4     3  8, 16, 20
  5     6  5, 10, 15, 25, 30, 35
  6     9  18, 24, 36, 42, 48, 54, 60, 66, 72
  7    12  7, 14, 21, 28, 49, 56, 63, 70, 77, 84, 91, 98

Rémy Sigrist, Table of n, a(n) for n = 1..10021
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A001462, A075383, A376904 (inverse), A376905, A377093.

PARI
```
\\ See Links section.
```

from itertools import count, islice
def A376903gen(): # generator of terms
    aset, alst = {1, 2, 4}, [1, 2, 4]
    yield from [1, 2, 4]
    for n in count(3):
        nlst = []
        for k in count(n, n):
            if k not in aset:
                nlst.append(k)
                if len(nlst) == alst[n-1]:
                    break
        yield from nlst
        alst.extend(nlst)
        aset.update(nlst)
print(list(islice(A376903gen(), 100))) # Michael S. Branicky, Oct 16 2024

A376905 Lexicographically earliest sequence of distinct positive integers with a(1) multiples of a number b(1) followed by a(2) multiples of a number b(2) etc.

Original entry on oeis.org

1, 2, 4, 3, 6, 9, 12, 5, 10, 15, 7, 14, 21, 28, 35, 42, 8, 16, 24, 32, 40, 48, 56, 64, 72, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 13, 26, 39, 52, 65, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 18, 36, 54, 90, 108, 126, 144, 162, 180, 198, 216

Offset: 1

Rémy Sigrist, Oct 08 2024

This sequence combines features of Golomb's sequence (A001462) and A361748.
This sequence is a permutation of the positive integers with inverse A376904.
This sequence can also be seen as an irregular table whose n-th row contains a(n) multiples of its leading term.

			The first terms/rows are:
  n  a(n)  b(n)  n-th row
  -  ----  ----  -------------------------------------------------
  1     1     1  1
  2     2     2  2, 4
  3     4     3  3, 6, 9, 12
  4     3     5  5, 10, 15
  5     6     7  7, 14, 21, 28, 35, 42
  6     9     8  8, 16, 24, 32, 40, 48, 56, 64, 72
  7    12    11  11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132
  8     5    13  13, 26, 39, 52, 65
  9    10    17  17, 34, 51, 68, 85, 102, 119, 136, 153, 170

Rémy Sigrist, Table of n, a(n) for n = 1..10063
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A001462, A361748, A376903, A376906 (inverse), A377093.

PARI
```
\\ See Links section.
```

from itertools import count, islice
def A376905gen(): # generator of terms
    aset, alst, m = {1, 2, 4}, [1, 2, 4], 3
    yield from [1, 2, 4]
    for n in count(3):
        nlst = []
        for k in count(m, m):
            if k not in aset:
                nlst.append(k)
                if len(nlst) == alst[n-1]:
                    break
        yield from nlst
        alst.extend(nlst)
        aset.update(nlst)
        while m in aset: m += 1
print(list(islice(A376905gen(), 70))) # Michael S. Branicky, Oct 16 2024

cp's OEIS Frontend

A377094 Inverse permutation to A377093.

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A376903 Lexicographically earliest sequence of distinct positive integers with a(1) multiples of 1 followed by a(2) multiples of 2 etc.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python

A376905 Lexicographically earliest sequence of distinct positive integers with a(1) multiples of a number b(1) followed by a(2) multiples of a number b(2) etc.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python