cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A376906 Inverse permutation to A376905.

Original entry on oeis.org

1, 2, 4, 3, 8, 5, 11, 17, 6, 9, 26, 7, 38, 12, 10, 18, 43, 53, 68, 75, 13, 27, 89, 19, 110, 39, 138, 14, 173, 215, 223, 20, 28, 44, 15, 54, 239, 69, 40, 21, 263, 16, 295, 29, 335, 90, 383, 22, 439, 111, 45, 41, 503, 55, 30, 23, 70, 174, 575, 76, 586, 224, 608
Offset: 1

Views

Author

Rémy Sigrist, Oct 16 2024

Keywords

Examples

			A376905(42) = 65, so a(65) = 42.

Links

Crossrefs

Cf. A376905.

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

Views

Author

Rémy Sigrist, Oct 08 2024

Keywords

Comments

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.

Examples

			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

Links

Crossrefs

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

Programs

  • PARI
    \\ See Links section.
  • Python
    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

A377093 Irregular table read by rows; for any n > 0, let u(n) be the least positive integer not among the first n-1 rows; the n-th row lists the u(n) least multiples of u(n) not yet in the sequence.

Original entry on oeis.org

1, 2, 4, 3, 6, 9, 5, 10, 15, 20, 25, 7, 14, 21, 28, 35, 42, 49, 8, 16, 24, 32, 40, 48, 56, 64, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 12, 36, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 169, 182
Offset: 1

Views

Author

Rémy Sigrist, Oct 16 2024

Keywords

Comments

This sequence combines features of Golomb's sequence (A001462) and A361748.
This sequence is a permutation of the positive integers with inverse A377094.

Examples

			The first rows are:
    1;
    2, 4;
    3, 6, 9;
    5, 10, 15, 20, 25;
    7, 14, 21, 28, 35, 42, 49;
    8, 16, 24, 32, 40, 48, 56, 64;
    11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121;
    12, 36, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168;
    ...

Links

Crossrefs

Cf. A001462, A361748, A376903, A376905, A377094 (inverse).

Programs

  • PARI
    \\ See Links section.
  • Python
    from itertools import count, islice
def A377093gen(): # 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) == m:
                    break
        yield from nlst
        alst.extend(nlst)
        aset.update(nlst)
        while m in aset: m += 1
print(list(islice(A377093gen(), 70))) # Michael S. Branicky, Oct 16 2024
Showing 1-3 of 3 results.

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