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A338618 Lexicographically earliest sequence of distinct positive integers such that three consecutive terms are never pairwise coprime. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

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

Rémy Sigrist, PARI program for A338618

EXAMPLE

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

PROG

(PARI) See Links section.

CROSSREFS

See A338619 for a similar sequence.

Cf. A084937, A098550.

Sequence in context: A343012 A143692 A337116 * A114792 A113324 A338362

Adjacent sequences:  A338615 A338616 A338617 * A338619 A338620 A338621

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Nov 04 2020

STATUS

approved

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Last modified September 24 19:49 EDT 2022. Contains 356949 sequences. (Running on oeis4.)