A366021 a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) and, if a(n) < n, with a(n - a(n)).

1, 2, 4, 6, 8, 10, 12, 9, 15, 3, 18, 14, 16, 20, 22, 24, 21, 27, 30, 25, 35, 28, 26, 32, 34, 36, 33, 39, 42, 38, 40, 44, 46, 48, 45, 5, 50, 52, 54, 51, 57, 60, 55, 65, 70, 49, 56, 58, 62, 64, 66, 63, 7, 77, 84, 68, 17, 85, 75, 69, 72, 74, 76, 78, 80, 82, 86, 88, 90, 81, 87, 93, 96, 92, 94, 98

Offset

1,2

Comments

The majority of terms lie near the line a(n) = 1.1*n. The only exceptions are the prime valued terms whose appearance in the sequence is delayed relative to their magnitude, e.g. a(1835) = 61. Other than the first two terms there are no other fixed points in the first 100000 terms, and it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000.

Example

a(5) = 8 as 8 shares a factor with a(4) = 6 and, as 8 > 5, it is not required to share a factor with any previous term. Note that 3 also shares a factor with 6, but as 3 < 5 it is required to share a factor with a(5-3) = a(2) = 2 which is does not, so a(5) cannot be 3. This is the first term to differ from A064413.
a(10) = 3 as 3 shares a factor with a(9) = 15 and, as 3 < 10, it is required to share a factor with a(10-3) = a(7) = 12, which it does.

Crossrefs

Cf. A064413, A027748, A365259, A365453.

Sequence in context: A319807 A055954 A379248 * A365453 A365984 A301454

Adjacent sequences: A366018 A366019 A366020 * A366022 A366023 A366024

Keyword

nonn

Author

Scott R. Shannon, Sep 26 2023

Status

approved