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A320123 a(1) = 1, a(2) = 2, a(3) = 3, and for any n > 3, a(n) = the smallest positive integer not yet in the sequence such that gcd(a(n-2), a(n-1)), gcd(a(n-1), a(n)) and gcd(a(n), a(n-2)) are all distinct. 1
1, 2, 3, 6, 4, 9, 12, 8, 15, 10, 14, 5, 20, 16, 25, 30, 18, 27, 22, 24, 11, 33, 21, 7, 36, 28, 35, 26, 40, 13, 52, 32, 39, 42, 34, 17, 38, 68, 19, 76, 44, 55, 45, 48, 46, 23, 50, 92, 60, 51, 56, 54, 49, 63, 57, 70, 66, 65, 75, 69, 80, 72, 78, 64, 81, 84, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is a variant of A127202.

The sequence is well defined as for any n > 3, provided the first n terms are known, any number v of the form a(n-2) * b where b is coprime to a(n) * a(n-1) satisfies #{ gcd(a(n-1), a(n)), gcd(a(n), v), gcd(v, a(n-1)) } = #{ gcd(a(n-1), a(n)), gcd(a(n), a(n-2)), gcd(a(n-2), a(n-1)) } = 3, and a(n+1) exists.

In the scatterplot of the sequence, the prime numbers correspond to the lower line.

LINKS

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

Rémy Sigrist, PARI program for A320123

EXAMPLE

The first terms, alongside gcd(a(n-2), a(n-1)), gcd(a(n-1), a(n)) and gcd(a(n), a(n-2)), are:

  n   a(n)  gcd(a(n-2),a(n-1))  gcd(a(n-1),a(n))  gcd(a(n),a(n-2))

  --  ----  ------------------  ----------------  ----------------

   1     1                 N/A               N/A               N/A

   2     2                 N/A                 1               N/A

   3     3                   1                 1                 1

   4     6                   1                 3                 2

   5     4                   3                 2                 1

   6     9                   2                 1                 3

   7    12                   1                 3                 4

   8     8                   3                 4                 1

   9    15                   4                 1                 3

  10    10                   1                 5                 2

  11    14                   5                 2                 1

  12     5                   2                 1                 5

  13    20                   1                 5                 2

  14    16                   5                 4                 1

  15    25                   4                 1                 5

PROG

(PARI) See Links section.

CROSSREFS

Cf. A127202.

Sequence in context: A152679 A232561 A348395 * A194357 A165783 A354046

Adjacent sequences:  A320120 A320121 A320122 * A320124 A320125 A320126

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Oct 06 2018

STATUS

approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)