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.

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

1,2

Comments

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.

Links

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

Example

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

Prog

(Python)
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
(PARI) \\ See Links section.

Crossrefs

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

Sequence in context: A338919 A348018 A363504 * A332878 A376903 A113233

Adjacent sequences: A376902 A376903 A376904 * A376906 A376907 A376908

Keyword

nonn,tabf

Author

Rémy Sigrist, Oct 08 2024

Status

approved