A376903 - OEIS

A376903

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

LINKS

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

EXAMPLE

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

PROG

(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

CROSSREFS

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

Sequence in context: A363504 A376905 A332878 * A113233 A051849 A283961

Adjacent sequences: A376900 A376901 A376902 * A376904 A376905 A376906

KEYWORD

nonn,tabf

AUTHOR

Rémy Sigrist, Oct 08 2024

STATUS

approved