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
Examples
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.
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A100795.
Programs
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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]", ")) }
Comments