|
| |
|
|
A354575
|
|
a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is coprime to a(n-1) and the difference a(n) - a(n-1) is distinct from all previous differences.
|
|
4
|
|
|
|
1, 2, 5, 3, 7, 4, 9, 8, 15, 11, 6, 17, 10, 19, 13, 21, 23, 12, 25, 16, 31, 14, 33, 20, 37, 18, 41, 26, 47, 22, 49, 27, 43, 29, 35, 53, 24, 55, 28, 57, 34, 59, 38, 71, 30, 67, 32, 73, 36, 79, 39, 61, 45, 77, 46, 81, 91, 40, 87, 44, 83, 50, 99, 52, 97, 42, 95, 51, 65, 89, 63, 101, 48, 103, 54, 113
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
This sequence uses a similar rule to A354688 but here the sign of the difference between a(n-1) and a(n) is considered. This leads to the terms showing much more erratic behavior than A354688; see the linked image.
In the first 200000 terms the fixed points are 1,2,8,35, and it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.
See A354679 for the differences between terms.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
a(9) = 15 as a(8) = 8, and 15 is the smallest unused number that is coprime to 8 and whose difference from the previous term, 15 - 8 = 7, has not appeared. Note that 11 and 13 are coprime to 8 but their differences from 8, namely 3 and 5, have already appeared as differences between previous pairs of terms.
a(15) = 13 as a(14) = 19, and 13 is the smallest unused number that is coprime to 19 and whose difference from the previous term, 13 - 19 = -6, has not appeared. Note that 12 is coprime to 19 and smaller than 13 but its difference from 19, namely -7, has already appeared as a difference between a(13) and a(12).
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
