A338619 -id:A338619 - cp's OEIS frontend

A338618 Lexicographically earliest sequence of distinct positive integers such that three consecutive terms are never pairwise coprime.

1, 2, 4, 3, 6, 5, 8, 10, 7, 12, 9, 11, 15, 18, 13, 14, 16, 17, 20, 22, 19, 24, 21, 23, 27, 30, 25, 26, 28, 29, 32, 34, 31, 36, 33, 35, 39, 40, 38, 37, 42, 44, 41, 46, 48, 43, 45, 50, 47, 52, 54, 49, 51, 56, 57, 58, 60, 53, 55, 65, 59, 70, 62, 61, 64, 66, 63

Offset: 1

Rémy Sigrist, Nov 04 2020

nonn

In other words, for any n > 0, at least one of gcd(a(n), a(n+1)), gcd(a(n), a(n+2)), gcd(a(n+1), a(n+2)) is strictly greater than 1.
This sequence has connections with the Yellowstone permutation (A098550).
Conjecture: this sequence is a permutation of the natural numbers.

			The first terms, alongside associated GCD's, are:
  n   a(n)  gcd(a(n),a(n+1))  gcd(a(n),a(n+2))  gcd(a(n+1),a(n+2))
  --  ----  ----------------  ----------------  ------------------
   1     1                 1                 1                   2
   2     2                 2                 1                   1
   3     4                 1                 2                   3
   4     3                 3                 1                   1
   5     6                 1                 2                   1
   6     5                 1                 5                   2
   7     8                 2                 1                   1
   8    10                 1                 2                   1
   9     7                 1                 1                   3
  10    12                 3                 1                   1

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A338618

See A338619 for a similar sequence.

Cf. A084937, A098550.

PARI
```
See Links section.
```

cp's OEIS Frontend

A338618 Lexicographically earliest sequence of distinct positive integers such that three consecutive terms are never pairwise coprime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI