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.

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

Author

Rémy Sigrist, Oct 16 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 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

• Rémy Sigrist, Table of n, a(n) for n = 1..10258
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

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