A354727 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) and the difference a(n) - a(n-1) is distinct from all previous differences.

1, 2, 4, 8, 6, 3, 9, 12, 20, 5, 10, 22, 11, 33, 15, 24, 14, 7, 21, 28, 16, 26, 13, 39, 18, 34, 17, 51, 27, 42, 36, 32, 50, 25, 45, 40, 64, 30, 55, 35, 56, 48, 75, 66, 38, 19, 57, 76, 44, 72, 46, 23, 69, 92, 52, 65, 95, 60, 93, 31, 62, 94, 47, 141, 54, 90, 63, 49, 84, 68, 85, 125, 70, 112, 58

Offset

1,2

Comments

This sequences uses similar a similar rule to A354687 but here the sign of the difference between a(n-1) and a(n) is considered. The terms show an overall similar behavior to A354687 although here only two lines show a higher concentration of terms than the other lines. See the linked image.

In the first 100000 terms the fixed points are 1,2,15,32,100,115,300,720. It is plausible no more exist although this is unknown.. The sequence is conjectured to be a permutation of the positive integers.

See A354739 for the differences between terms.

Links

Table of n, a(n) for n=1..75.

Scott R. Shannon, Image of the first 100000 terms. The green line is y = n.

Example

a(9) = 20 as a(8) = 12, and 20 is the smallest unused number that shares a factor with 12 and whose difference from the previous term, 20 - 12 = 8, has not appeared. Note that 10,14,15,16,18 all share a factor with 12 but their differences from 12, namely -2,2,3,4,6, have already appeared as differences between previous pairs of terms.

Crossrefs

Cf. A354739, A354687, A354575, A354679, A354688.

Sequence in context: A080868 A046260 A254065 * A329455 A292808 A300813

Adjacent sequences: A354724 A354725 A354726 * A354728 A354729 A354730

Keyword

nonn

Author

Scott R. Shannon, Jun 05 2022

Status

approved