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

Author

Rémy Sigrist, Oct 08 2024

Keywords

• nonn
• tabf

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.

Examples

			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
		

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

Crossrefs

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

Programs

PARI

\\ See Links section.

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