A378098 Lexicographically earliest sequence of distinct positive integers such that a(a(n)) shares a factor with a(a(n)-1).

2, 4, 5, 10, 6, 8, 9, 12, 14, 16, 13, 26, 18, 15, 20, 22, 19, 38, 24, 21, 27, 30, 25, 35, 28, 32, 34, 36, 23, 46, 33, 39, 42, 40, 44, 48, 41, 82, 50, 45, 51, 54, 47, 94, 52, 56, 49, 63, 57, 60, 55, 65, 58, 62, 64, 66, 68, 70, 61, 122, 72, 69, 75, 78, 74, 76, 71, 142, 80, 84, 77, 88, 79, 158, 86, 90, 81, 87, 93, 96, 92, 98, 85, 95, 100, 102, 99, 105, 91, 104

Offset

1,1

Comments

A self-referencing EKG-type sequence. The terms appear to be concentrated along two lines, a lower straight line where a(n) is slightly above n and an upper straight line where a(n) is approximately 2*n. For larger values of n the later line is composed solely of even semiprimes.

In the first 100000 terms there are no fixed points, and it is likely none exist. In the same range there are only two terms where a(n) is less than n, for a(29) = 23 and a(97) = 89.

The missing numbers are 1, 3, 7, 11, 17, 29, 31, 37, 43, 53, 59, 67, 73, 83, ... .

Links

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

Example

a(2) = 4 as a(1) = 2 and 4 is the smallest unused number that shares a factor with a(2-1) = a(1) = 2.
a(3) = 5 as a(3) is not referenced earlier in the sequence so it is the lowest unused number that does not violate the sharing factor requirement. It cannot be 3 as that would require a(3) = 3 to share a factor with a(3-1) = a(2) = 4, which is does not, and it cannot be 4 as that has already been used.

Crossrefs

Cf. A064413, A378030, A121053, A027746.

Sequence in context: A122991 A245512 A366351 * A232616 A125728 A351871

Adjacent sequences: A378095 A378096 A378097 * A378099 A378100 A378101

Keyword

nonn

Author

Scott R. Shannon, Nov 16 2024

Status

approved