A358201 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with sigma(max_{k=1..n-1}a(k)).

1, 2, 3, 4, 7, 6, 8, 5, 9, 13, 10, 12, 14, 15, 16, 31, 18, 20, 22, 24, 26, 28, 30, 32, 21, 27, 33, 34, 36, 35, 39, 38, 40, 25, 42, 44, 45, 46, 48, 50, 51, 52, 49, 54, 55, 56, 57, 58, 60, 62, 63, 64, 127, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108

Offset

1,2

Comments

The sequence is conjectured to be a permutation of the positive integers. In the first 150000 terms the fixed points are 1, 2, 3, 4, 6, 9, 12, 93, 6003, 6881, 16269, 100707, 114839, 116999. It is likely more exist.

Links

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

Scott R. Shannon, Image of the first 150000 terms. The green line is a(n) = n.

Example

a(9) = 9 as sigma(max_{k=1..8}a(k)) = sigma(8) = A000203(8) = 15, and 9 is the smallest unused number that shares a factor with 15.

Crossrefs

Cf. A000203, A358176, A358082, A064413, A356851, A356430, A354960.

Sequence in context: A247798 A130685 A210202 * A358176 A359682 A260436

Adjacent sequences: A358198 A358199 A358200 * A358202 A358203 A358204

Keyword

nonn,look

Author

Scott R. Shannon, Nov 03 2022

Status

approved