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A282291 Lexicographically earliest sequence of distinct terms such that every pair of consecutive terms contains a term that is an unitary divisor of the other term. 2
1, 2, 6, 3, 12, 4, 20, 5, 10, 30, 15, 60, 420, 7, 14, 42, 21, 84, 28, 140, 35, 70, 210, 105, 840, 8, 24, 120, 40, 280, 56, 168, 1848, 11, 22, 66, 33, 132, 44, 220, 55, 110, 330, 165, 660, 4620, 77, 154, 462, 231, 924, 308, 1540, 385, 770, 2310, 1155, 9240, 88 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence has connections with A113552 and A281978: each pair of consecutive terms contains a term that divides the other term.

The derived sequence A282304 gives some insights about the fractal nature of this sequence.

Conjectures:

- All prime numbers appear in this sequence, in increasing order,

- The derived sequence A282304 is unbounded,

- This sequence is a permutation of the natural numbers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Logarithmic scatterplot of the first 250000 terms (the two blue sections are equal up to a scaling factor of 47)

Rémy Sigrist, PARI program for A282291

EXAMPLE

The first terms, alongside their p-adic valuations with respect to p=2, 3, 5 and 7 (with 0's omitted), are:

n  a(n)  v2 v3 v5 v7

-- ----  -- -- -- --

1     1

2     2   1

3     6   1  1

4     3      1

5    12   2  1

6     4   2

7    20   2     1

8     5         1

9    10   1     1

10   30   1  1  1

11   15      1  1

12   60   2  1  1

13  420   2  1  1  1

14    7            1

15   14   1        1

16   42   1  1     1

17   21      1     1

18   84   2  1     1

19   28   2        1

20  140   2     1  1

21   35         1  1

22   70   1     1  1

23  210   1  1  1  1

24  105      1  1  1

25  840   3  1  1  1

MATHEMATICA

a = {1}; Do[k = 1; While[Or[MemberQ[a, k], Nand[Divisible[#2, #1], CoprimeQ[#1, #2/#1]]] & @@ Sort@ # &@{k, Last@ a}, k++]; AppendTo[a, k], {n, 58}]; a (* Michael De Vlieger, Feb 12 2017 *)

CROSSREFS

Cf. A113552, A281978, A282304.

Sequence in context: A253279 A297076 A113552 * A176352 A064736 A243618

Adjacent sequences:  A282288 A282289 A282290 * A282292 A282293 A282294

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Feb 11 2017

STATUS

approved

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Last modified February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)