A336215 Lexicographically earliest sequence of positive integers such that for any k > 0, there are k occurrences of k in the sequence, and the distance between any two occurrences of k is a multiple of k.

1, 2, 3, 2, 4, 3, 5, 6, 3, 7, 8, 5, 4, 6, 9, 10, 4, 11, 8, 6, 4, 5, 12, 7, 13, 6, 5, 14, 11, 15, 7, 5, 9, 16, 8, 10, 17, 6, 18, 11, 19, 9, 8, 6, 7, 10, 12, 20, 21, 16, 8, 7, 22, 17, 23, 10, 18, 24, 7, 9, 25, 11, 26, 13, 27, 7, 8, 20, 9, 14, 12, 28, 11, 29, 8

Offset

1,2

Comments

This sequence has similarities with A100795.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

For k = 1:
- we can set a(1) = 1,
For k = 2:
- we can set a(2) = a(4) = 2,
For k = 3:
- we can set a(3) = a(6) = a(9) = 3.
For k = 4:
- we can set a(5) = 4,
- however a(9) is already set to 3,
- so we continue with a(13) = a(17) = a(21) = 4.

Prog

(PARI) { v=1; for (n=1, #a=vector(75), if (!a[n], r=v; forstep (m=n, #a, v, if (!a[m], a[m]=v; if (!r--, break))); v++; ); print1 (a[n]", ")) }

Crossrefs

Cf. A100795.

Sequence in context: A054384 A026400 A026409 * A243290 A085238 A214371

Adjacent sequences: A336212 A336213 A336214 * A336216 A336217 A336218

Keyword

nonn,look

Author

Rémy Sigrist, Jul 12 2020

Status

approved